I always thought the "general" advice for a foreign visitor to the Carib seeking to avoid U.S. visa fees was Canada. No-fee transit visa...yet enough flights into the Caribbean that you could do it without an insane routing that would kill off any advantage gained by avoiding the U.S. I'm pretty sure we've had this question a couple times before, although not necessary specifically about Indian travelers.

I guess another option would be a one-stop through Europe landing on one of the islands in the Caribbean that has a direct AF, BA, KLM, etc. flight. Then connect to a local short-hop carrier to get you to Jamaica. (Probably as a separate ticket.) Might be a lot more time-efficient overall...seems like visa requirements once you're in the Caribbean are more of the obtained-at-the-airport variety.