FindMyPast has military records for -
1851 Worldwide Index - James Judge, No. 2177, Drummer and Fifer, 1st Battalion Rifle Brigade, location Dover, period 1/1/1851 - 31/3/1851
Medals and Awards 1857-1859 - James Judge, No. 11, Bugle Major, Clasp - Lucknow, Indian Mutiny Medal
1861 Worldwide Index - James Judge, No. 11, Serjeant, 3rd Battalion Rifle Brigade, location Bareilly East Indies
Baptisms
Born Jul 18th 1860, baptised Sep 30th 1860, Arthur Henry, boy, parents James and Sarah Anne Judge, profession - Sergeant Commissariat Department, place Muttra, India
Possibly the same James?
The 1851 Census has James Judge, age 30, bugler, 91st Rifles, born Westmeath