Fencible Infantry:

Princess of Wales' (Aberdeen Highland) Regiment.[Aberdeen Fencible Regiment of Foot] : Scotts.
Highland dress. Facings yellow; Colonel Sir James Leith (8 August 1763 – 16 October 1816): Raised 25 October 1794; Disbanded 11 September 1803; Raised 25 October 1794. Embodied at Aberdeen. Disbanded in Ireland, 11 September 1803.
https://en.wikipedia.org/wiki/James_Leith_(British_Army_officer)
“Leith soon returned home, where on 25 October 1794 he was authorized to raise a regiment of Fencibles. The regiment was presented with its colours on 22 July 1795, and added to the Army establishment the following day as the Aberdeen Fencible Regiment of Foot, but was renamed the Princess of Wales's, or Aberdeen Highland Fencible Infantry later in the year. In August 1795 Leith was brevetted colonel, with the rank of lieutenant-colonel in the army. His regiment was stationed in Ireland, seeing action during the 1798 Rebellion.[9] Leith was promoted to colonel in the army on 1 January 1801, and his regiment was finally disbanded at Naas in April 1803.”
“His services having now obtained for him the rank of major, by brevet, Mr. Leith procured leave to raise the “Aberdeenshire Fencibles :” at the head of which regiment her served for some years in Ireland. “During the rebellion.” we are told. “he was conspicuous for his activity and firmness of mind, and those qualities that found full scope for development in the mercy and forgiveness extended to many of the objects of mistaken feeling, whom circumstances placed in his power ; – and it is no slight eulogium, that during scenes, where so much bloodshed was inevitable, Colonel Leith’s humanity never became in the slightest degree questioned.’ ”

Angusshire Regiment: Scotts.
“Facings yellow; Colonel Archibald [James Edward] Douglas (1748–1827); Raised 20 October 1794; Disbanded 19 July 1802;
Had a good many Highlanders from the Highland borders. Served in Ireland. Disbanded at Perth.”
http://douglashistory.co.uk/history/Regiments/Angus_Regiment_Fencibles.htm#.Xd7RY25Fweg

“2nd Argyllshire Regiment: Scotts.
Highland dress. Facings Blue; Colonel Henry Mord[aunt] Clavering (1759-1850); Raised 25 October 1794; Disbanded 24 July 1802; Served in Ireland. Disbanded at Ayr.”
http://www.thepeerage.com/p1947.htm https://www.npg.org.uk/collections/search/portrait/mw69964

Breadalbane Regiment — 2nd Battalion: Scotts.
“Lieutenant-Colonel Andrew Macdouall of Logan (December 7, 1758 - May 3, 1834); Lt.-col. Wigtown vols. 1803-9:
Raised 8 March 1793; Disbanded 18 April 1799: Embodied at Perth. In 1798 the greater part of this corps volunteered for service in Ireland, and landed at Carrickfergus in September. Returned to Scotland in March 1799. Disbanded at Paisley.”
http://www.rootschat.com/forum/index.php?topic=387245.0

Breadalbane Regiment — 3rd Battalion: Scotts.
Lieutenant-Colonel John Campbell of Achallader (30 March 1762 – 29 March 1834); Raised 9 December 1794; Disbanded 28 July 1802; Served in Ireland. Disbanded at Ayr.
https://en.wikipedia.org/wiki/John_Campbell,_1st_Marquess_of_Breadalbane http://www.thepeerage.com/p1360.htm#i13596

Caithness Legion. Scotts:
The bonnet and tartan pantaloons (truis). Facings yellow; Colonel Sir Benjamin Dunbar of Hempriggs (April 28, 1761 - May 1843); Raised 15 November 1794; Disbanded 1802; Served in Ireland. Disbanded at Enniscorthy.
https://www.geni.com/people/Sir-Benjamin-Sutherland-Dunbar-6th-Lord-Duffus/6000000017140111871
“... as heir-male, assumed the title on the death of James, Lord Duffus, in 1827.”

Cheshire: English.
Colonel Charles Courtenay; Raised 17 November 1794; Dis banded 1801–2: Ten companies.

Devon and Cornwall: English.
Colonel Robert Hall; Raised 15 November 1794; Disbanded 1801–2; Ten companies.

Inverness-shire Fencibles [Duke of York's Royal Inverness-shire Highlanders]: Scotts.
Highland dress. Initially buff facings, became blue facings when they became the Duke of York's;
Colonel John Baillie of Dunean; Raised 21 November 1794; Disbanded 25 August 1802;
Embodied at Inverness. Served in Ireland during the Irish Rebellion of 1798, and after its suppression the designation of the corps was changed to "The Duke of York's Royal Inverness-shire Highlanders" as a compliment to their good behaviour.
“The regiment was immediately ordered to Ireland, and with such haste that the men were despatched without clothing or arms, of which, however, they received a supply at Glasgow on their route. The regiment was actively employed during the rebellion, and conducted themselves in that unfortunate service with as much forbearance as circumstances would permit. Colonel Baillie died in 1797, and was succeeded by Lieutenant-colonel Cumming Gordon [John Gordon Cuming > colonel 6.ii.1797].”:
https://en.wikipedia.org/wiki/Highland_Fencible_Corps#Inverness-shire_Fencibles_.281794.29
Bio: John Gordon-Cuming-Skene, Lt. Gen. (1761 - 1828): https://archive.org/stream/genealogicalhera01byuburk#page/663/mode/1up

Dumbarton Fencibles: Scotts.
Lieutenant Colonel John Campbell of Achalader:
https://en.wikipedia.org/wiki/Highland_Fencible_Corps#Dumbarton_Fencibles_.281794.29
https://en.wikipedia.org/wiki/Colin_Campbell_(British_Army_officer,_born_1776)

Loyal Durham. English.
Green facings; Colonel Barrington Price (1758 - April 05, 1839); Raised 26 February 1795;Disbanded 1801–2; Ten companies. Served in Ireland during the rebellion.
https://www.geni.com/people/Colonel-Barrington-Price-of-Becket/6000000003485767438

Lord Elgin's Regiment. Scotts.
The bonnet and truis.[l] Facings green; Colonel Thomas Bruce, 7th earl of Elgin (20 July 1766 – 14 November 1841); Raised 28 November 1794: Disbanded 15 October 1802; There were about 300 Highlanders in this corps. Served in Ireland. Disbanded at Linlithgow.
https://en.wikipedia.org/wiki/Thomas_Bruce,_7th_Earl_of_Elgin

Loyal Essex; English.
Colonel John E. Urquhart; Raised 20 October 1794; Disbanded 1801–2; Ten companies. Served in Ireland during the rebellion.

Fifeshire Fencibles. Scotts.
Facings yellow; Colonel James Durham of Largo (January 14, 1754 - February 6, 1840); Raised 20 October 1794: Disbanded 11 April 1803: Served in Ireland. Disbanded at Kilkenny.
“... General James Durham of Largo, born January 14, 1754, who served in the army no less than seventy years, having entered as a cornet in the second dragoon guards, June 22, 1769. On the 21st of September 1794 he received the brevet of major; and, having raised the Fifeshire Fencibles, he was appointed lieutenant-colonel of that corps, October 23, 1794. From March 1804 to December 1808, he acted as brigadier and major-general in 1813, and that of general in 1830. He died February 6, 1840.”

Fraser Fencibles: Scotts.
Highland dress. Facings black; Colonel James Fraser of Belladrum (c1732-1808); [In November 1797, Colonel Fraser of Belladrum resigned, and Simon Fraser [John Simon Frederick Fraser (1765–1803): Capt. 1 (Strathspey) fencibles 1793; capt. Fraser’s fencibles 1795, col. 1797-1802.], the younger of Lovat, was appointed colonel.] Raised 29 November 1794; Disbanded 12 July 1802: Embodied at Inverness. of the soldiers, 300 bore the name of Fraser. Served in Ireland. Disbanded at Glasgow.
https://www.electricscotland.com/history/sketches/highlandsketches100.htm
https://en.wikipedia.org/wiki/Highland_Fencible_Corps#Fraser_Fencibles_(1794)
http://thepeerage.com/p70228.htm#i702275
“He gained the rank of Lieutenant in 1759 in the 87th Regiment of Highland Volunteers. He gained the rank of Captain-Lieutenant on 8 October 1759. He gained the rank of Captain on 20 December 1760. He fought in the Seven Years War. He gained the rank of Major on 29 August 1777. He gained the rank of Major on 8 January 1779 in the Northern Regiment of Fencible Men. He gained the rank of Major on 8 April 1779 in the 2nd/71st Foot (Fraser's Highlanders). He gained the rank of Colonel in 1797 in the Fraser Fencibles.”
“The Fraser Fencible Regiment was raised by Col. the Hon. Archibald Campbell Fraser of Lovat (16 August 1736 – 8 December 1815), as a home guard in the event of an invasion by Napoleon Bonaparte. The Fraser Fencibles served in the Irish Rebellion of 1798. ”
https://en.wikipedia.org/wiki/John_Simon_Frederick_Fraser https://www.historyofparliamentonline.org/volume/1790-1820/member/fraser-john-simon-frederick-1765-1803

Glengarry Fencibles: Scotts.
Highland dress. Facings yellow; Colonel Alex. Macdonnell of Glengarry; Raised 14 August 1794: Disbanded 1 July 1802; Raised as a Catholic corps. According to General Stewart, more than one-half of the men in this regiment were enlisted from the estate of Glengarry. Of the thirty-two officers, twenty-two were Macdonnells or Macdonalds. Served in Jersey, Guernsey, and in Ireland, where they were actively employed during the rebellion, earning for themselves the sobriquet of the "Devil's Bloodhounds".[m] Disbanded at Ayr, after which the greater part of the regiment emigrated, together with their families and relations, to Canada, settling in a district to which they gave the name of their native glen.
“In the summer of 1798 the Glengarry Fencibles moved to Ireland. On landing at Balleback , they marched to Waterford, and thence to New Ross the same day.”:
https://en.wikipedia.org/wiki/Highland_Fencible_Corps#Glengarry_Fencibles_.281794.29

Prince of Wales' Leicester. English.
Major Parkyns; Raised 15 November 1794; Disbanded 1801–2; Ten companies. Served in Ireland during the rebellion.

Royal Manx Regiment (2nd Battalion): Manx.
Blue facings, fur crest around hat; Colonel Duke of Atholl; Raised 7 April 1795; Disbanded 1801–2; Second corps. Ten companies. The 2nd Battalion served in Ireland. Some of the men in this battalion were recruited in return and the list of officers shows a few names which suggests a connection with Perthshire.

Northampton: English.
Blue facings red collar; Colonel John Manners Ker; Raised 20 October 1794; Disbanded 1801–2; Ten companies. Served in Ireland during the rebellion.

Northumberland [Northumberland Francis]: English.
Colonel Blake; Raised 28 February 1795; Disbanded 1801–2; Ten companies.

North Lowland Regiment: Scotts.
Facings green; Colonel Thomas Balfour; Raised November 1794; Disbanded 6 August 1802;
There were a number of Highlanders in this corps. Served in Ireland. Disbanded at Dundee.

Loyal Nottingham: English.
Green facings; Colonel James O'Connor; Raised 20 October 1794; Disbanded 1801–2: Ten companies. Served in Ireland during the rebellion.

Perthshire Highlanders: Scotts.
Facings yellow; Colonel William Robertson of Lude; Raised 20 October 1794; Disbanded 27 February 1799; Embodied at Perth. "Although called Perthshire Highlanders, this was a misnomer, as the number of Perthshire Highlanders, or Highlanders of any county, was very limited". Disbanded at Preston.

Reay Highland Regiment: Scotts.
Highland dress. Facings light grey-blue; Colonel Mackay Hugh Baillie of Rosehall; Raised 24 October 1794; Disbanded 13 October 1802; Embodied at Elgin. Served in Ireland. Was present at the battles of Tara Hill and Ballinamuck. Disbanded at Stirling.

Rothesay and Caithness Highlanders — 2nd Battalion. Scotts.
Highland dress. Facings yellow; Lieutenant-Colonel Benjamin Williamson; Raised 19 November 1794; Disbanded July 1802: Embodied at Forfar. Served in Ireland for two years, where it was distinguished for its exemplary conduct. In 1797 this battalion volunteered for service in any part of Europe, but was not called upon to go abroad. Disbanded at Glasgow.

Loyal Somerset: English.
Yellow facings; Colonel W. F. Forster; Raised 20 October 1794; Disbanded 1801–2; Ten companies. Served in Ireland during the rebellion

Suffolk: English.
Colonel John Robinson; Raised 20 October 1794; Disbanded 1801–2; Ten companies. Served in Ireland during the rebellion.

Sutherland Regiment. Scotts.
Highland dress. Facings yellow; Colonel Major-general William Wemyss of Wemyss; Raised 2 March 1793; Disbanded March 1799; Embodied at Fort George. Extended its services to Ireland in 1797. Disbanded at Fort George, many of the officers and men transferring their services to the 93rd Sutherland Highlanders, raised by General Wemyss on a letter of service dated 16 April 1799.

The Loyal Tay Regiment. Scotts.
Facings blue; Colonel Sir Robert Anstruther, Bart.; Raised 25 October 1794; Disbanded 28 June 1802; This regiment had a good many Highlanders from the Highland borders. Served in Ireland. Disbanded at Stirling.

York; English.
Colonel Hon. G. A, C. Stapylton; Raised 20 October 1794; Disbanded 1801–2; Ten companies. Served in Ireland during the rebellion.

Served in Ireland but not on published OOB. Note: Maybe arrived after 1798:

Royal Lancashire: English.
[Thomas,] Lord Grey de Wilton; Raised 16 October 1794; Disbanded 1801–2; Ten companies. Served in Ireland during the rebellion.
Rawstone. An account of the regiments of the Royal Lancashire Militia, 1759 to 1870. 1874. 463 p. : https://archive.org/details/anaccountregime00rawsgoog See : https://archive.org/details/anaccountregime00rawsgoog/page/n53

Lochaber Fencibles: cotts.
Highland dress. Facings black; Colonel Donald Cameron of Lochiel; Raised 15 June 1798; Disbanded 26 June 1802; Embodied at Falkirk. Served in Ireland. Disbanded at Linlithgow.

Princess Charlotte of Wales' or Loyal Macleod Fencibles: Scotts.
Highland dress. Facings blue; Colonel John Macleod of Colbecks; Raised 15 June 1798; Disbanded 11 June 1802; Embodied at Elgin. Served in Ireland. Disbanded in England at Tynemouth Barracks.

Ross And Cromarty Rangers: Scotts.
Highland dress. Facings yellow; Colonel Lewis Mackenzie, Younger of Scatwell; Raised 8 August 1798; Disbanded 27 July 1802; Raised for service in any part of Europe. Embodied at Inverness. Served in Scotland and Ireland. Disbanded at Inverness.

English Militia:

Bedfordshire Regiment of Militia: Col. Francis Moore:

Royal Bucks (or the King’s own) Regiment of Militia: Col. George, Marquess of Buckingham (17 June 1753 – 11 February 1813):

South Devenshire Regiment of Militia: Col. John, Lord Rolle (1750-3 April 1842):
https://en.wikipedia.org/wiki/John_Rolle,_1st_Baron_Rolle

Dorsetshire Regiment of Militia: Col. George, Lord Rivers (1721-1803):
https://www.clevelandart.org/art/1971.2
http://www.thepeerage.com/p4567.htm

North Gloucestershire Regiment of Militia: Col. Robert Kingscote:

Herefordshire Regiment of Militia: Col. John Geers Cotterell (1757-1845):
http://www.historyofparliamentonline.org/volume/1820-1832/member/cotterell-sir-john-1757-1845

1st, or West Kent Regiment of Militia: Col. Richard James:
It was embodied again in 1793 [.xii.1792] for the French Revolutionary Wars, ranked as the 1st, and disembodied in [.iv.]1802.

Royal Lancashire Regiment of Militia: Col. Thomas Stanley:

Leicestershire Regiment of Militia: Col. George Pochin (1732-1798):
https://www.npg.org.uk/collections/search/portrait/mw202461/George-Pochin

Lincolnshire Regiment of Militia: Col. William, Viscount Milsintown:

East Suffolk Regiment of Militia: Col. Edward Goate:

West Suffolk Regiment of Militia: Col. George, Earl of Euston (14 January 1760 – 28 September 1844): https://en.wikipedia.org/wiki/George_FitzRoy,_4th_Duke_of_Grafton

Warwickshire Regiment of Militia: Col. Francis, Marquess of Hertford:

Worcestershire Regiment of Militia: Col. James Wakeman Newport (1764-c.1864):
http://www.artnet.com/artists/john-nost-sartorius/colonel-newport-and-his-hounds-in-an-extensive-15HS_wyfDR7NsHKlobFwxA2

Bibliography:

List of British fencible regiments: https://en.wikipedia.org/wiki/List_of_British_fencible_regiments

List of the officers of the several regiments and corps of fencible cavalry and infantry :
of the officers of the militia; of the corps and troops of gentlemen and yeomanry : and of the corps and companies of volunteer infantry. 1795. iv, 180 p. ; 22 cm.

List of the officers of the several regiments and corps of fencible cavalry and infantry - of the officers of the militia [&c.]. 22 June 1797. :

List of the officers of the several regiments and corps of fencible cavalry and infantry: of the officers of the militia: of the corps and troops of gentlemen and yeomanry cavalry: and of the corps and companies of volunteer infantry: with an index: also a list of the officers of the cavalry and infantry associations: with an index. [1800]

Rawstone. An account of the regiments of the Royal Lancashire Militia, 1759 to 1870. 1874. 463 p. : https://archive.org/details/anaccountregime00rawsgoog