The Bengal Calendar, for the year 1787 including a List of the Hon. and United East-India Company's Military Servants on the Bengal Establishment, page 281 The European Magazine, and London Review, Volume 11 for 1787 by the Philological Society of London:
1787: https://play.google.com/books/reader?id=0p9nnB5BDesC
1789: https://play.google.com/books/reader?id=s37v1RoCHgMC
The East India kalendar ... Containing complete and correct lists of the Company's civil, military, marine, law, and revenue establishments ....:
1792: https://archive.org/details/b2874844x
Lists of the officers of His Majesty's, and the Hon. Company's troops, serving under the presidency of Bombay. Adjutant General's Office. January 1st. 1798:
A List of the Officers of the Army, Ordnance and Medical Departments, serving under the Presidency of Fort St. George. 1st April 1822: https://books.google.com.au/books?id=uEMIAAAAQAAJ
Madras artillery records [1836-62], 1838:
Band 1: https://books.google.ca/books?id=ij4IAAAAQAAJ
Band 2: https://books.google.ca/books?id=vj4IAAAAQAAJ
Band 3: https://books.google.ca/books?id=E0QIAAAAQAAJ
Band 7: https://books.google.ca/books?id=GD8IAAAAQAAJ
Note: Gale has many more of the period, but you must have on-line access.
Biographic informations for officers serving. Note: covers all periods to date of publications. Index at end of each volume.
The East India Military Calendar: Containing the Services of General and Field Officers of the Indian Army. 3 vols. 1823-1826:
Vol. 1 (1823):
https://archive.org/stream/eastindiamilita01philgoog
https://books.google.com/books?id=GR2URX7SRQkC
https://books.google.com/books?id=-EbRAAAAMAAJ
Vol. 2 (1824):
https://books.google.com/books?id=fUfRAAAAMAAJ
https://books.google.com/books?id=srUIAAAAQAAJ
https://books.google.com/books?id=e_I8zCCqhV4C
Vol. 3 (1826):
https://archive.org/details/in.ernet.dli.2015.284261
https://books.google.com/books?id=MiTv2GT6MG8C
https://books.google.com/books?id=3UfRAAAAMAAJ