1st Madras (European) Fusiliers

Chronology

1742 Major Stringer Lawrence raised the first troops for the East India Company in Madras in 1742. By 1766 they had three regiments.
1746 known as East India Company European Regiment
1766 renamed 1st Madras Europeans
1774 became the 1st Madras European Regiment (1st & 2nd Battalions)
1799 became the The Madras European Regiment (single battalion)
1824 became the The Madras European Regiment (1st & 2nd Battalions)
1830 reduced to single battalion
1839 became the 1st Madras (European) Regiment
1843 became the 1st Madras (European) Fusiliers
1858 taken into the British Army as the 1st Madras Fusiliers
1861 became the 1st Royal Madras Fusiliers
1862 renamed 102nd Regiment of Foot (Royal Madras Fusiliers)
1881 merged with the 103rd Regiment of Foot and became 1st Battalion Royal Dublin Fusiliers
1922 disbanded on the formation of the Irish Free State

Wikipedia:

A sketch of the services of the Madras European Regiment during the Burmese War by Major John Butler (1839) Google Books
Historical Record of the Honourable East India Company's First Madras European Regiment: Containing an Account of the Establishment of Independent Companies in 1645; Their Formation Into a Regiment in 1748; and Its Subsequent Services to 1842 by James George Smith Neill, Staff Officer (1843). Page xvi of the introduction (at the very front of the book) mentions the recruitment in the early days of a few Swiss mercenaries, French prisoners of war (after their release), 400 Germans at the Cape of Good Hope in 1795 and more Germans in the Eastern Islands [Amboyna] in 1810. The Germans from South Africa are discussed in this India List post
Services of 102nd Regiment of Foot 1842-1867 by Colonel Thomas Raikes (1867)