Can I get a FAA medical certificate and apply in an Indian airline?
Well Air India is hiring qualified pilots here. The advertisement says you need a medical certificate issued by the DGCA. There is no mention of accepting an FAA certificate.

I'm not completely sure how it works in India but usually you need to get a medical certificate from the country in which the airline is based (or to be specific, the country in which the aircraft is registered). I'm not aware of any exceptions to this rule except for temporary operations, but I stand to be corrected.