British regular units in Ireland 1798 being reported in various works of1798:

2nd Regiment of Foot:
Cannon. Historical record of The Second, or, Queen's Royal Regiment of Foot. 1839. pp. 46-47:

6th Regiment of Foot:
Cannon. Historical record of the Sixth, or Royal First Warwickshire Regiment of Foot. 1839, pp. 74-75:

13th Regiment of Foot:
Cannon. Historical record of the Thirteenth, First Somerset, or the Prince Albert's Regiment of Light Infantry. 1848, pp. 45-46:

17th Regiment of Foot:
Historical record of the Seventeenth, or the Leicestershire Regiment of Foot. 1848, p. 30:

25th Regiment of Foot:
Higgins. The records of the King's own borderers, or, Old Edinburgh regiment. 1873, p. 206:

29th Regiment of Foot:
Everard. History of Thos. Farrington's Regiment Subsequently Designated the 29th (Worcestershire) Foot, 1694 to 1891. 1891, pp. 222-232:

60th Regiment of Foot:
A regimental chronicle and list of officers of the 60th, or the King's, royal rifle corps. 1879, pp. 3, 14, 23, 37-38, 47, 129-134:

64th Regiment of Foot:
“The regiment returned to England in 1795, before moving to Gibraltar and then Ireland, where it played a minor part in suppressing the 1798 rebellion. The 64th returned to England in 1800.” : Cook, Hugh (1970). The North Staffordshire Regiment (The Prince of Wales's). Famous Regiments. 1970, p. 26.

69th Regiment of Foot:
A Narrative of the Historical Events, Connected with the Sixty-ninth Regiment. 1870, pp. 122: Served with Royal Navy as marines in 1798.

92nd Highlanders:
Gardyne. The Life of a Regiment - The History of the Gordon Highlanders. Vol 1. 1901, pp. 46-59:

100th Regiment of Foot: The 100th Regiment of Foot was raised in Northern Ireland in 1804.

4th of Dragoon Guards:
Cannon. The Fourth; or, Royal Irish Regiment of Dragoon Guards, containing an account of the formation of the regiment in 1685 - and of its subsequent services to 1838. 1839, pp. 37-43:

5th Regiment of Dragoons:
Cannon. Historical record of the Fifth, or Princess Charlotte of Wales's Regiment of Dragoon Guards - containing an account of the formation of the regiment in 1685, with its subsequent services to 1838. 1839, pp. 46-48:

6th Regiment of Dragoon Guards:
Cannon. Historical record of the Sixth Regiment of Dragoon Guards, or the Carabineers. 1839, pp. 78-80. :

9th Regiment of (Light) Dragoons:
Cannon. Historical Record of the Ninth, or Royal Regiment of Light Dragoons, Lancers. 1841, pp. 24-29:

22nd Regiment of (Light) Dragoons:
Raymond Birt. XXII Dragoons 1760–1945: The Story of a Regiment. 1950. 349 p.:

24th Regiment of (Light) Dragoons: “The regiment was raised in 1795 as the 27th Regiment of (Light) Dragoons, being renumbered in 1803 as the 24th Regiment of (Light) Dragoons.”

The Royal Attillery:

Duncan, Major Francis. History of the Royal Regiment of Artillery. Vol II (1784-1815). 1879. 528 p. See pp. 75-87. : https://archive.org/details/historyofroyalre02duncuoft

Brigadier-General Paul A. Pakenham. GUNNER JAMES MAGEE, Defender of Values – The Artillery Corps – Óglaigh na hÉireann. September 2018 :
http://artilleryclub.ie/wp-content/uploads/2018/09/Gunner-Magee-Defender-of-Arty-Corps-Value
s-V-25-Sep-18-1.pdf