The father of Bridget Sophia McCormick born Bellary, India in 1867 was Private James McCormick of the 76th Regiment.
The Jane McCormick who died in Madras in 1865 (aged 1 year 5 months) was also a daughter of James McCormick of the 76th.
The other McCormick baptisms spotted by Gaffy were from a different family I think. That James was in an artillery unit.
FindMyPast has discharge papers for two James McCormicks of the 76th regiment. The most likely one was born Seagoe, Lurgan circa 1829. He intended to reside in Belfast on discharge in 1869. The other was born Colrey, Sligo around 1840 and intended to reside in Woolwich on discharge in 1878.