Now that you have clarified some things I think you should mention it, so you don't have a gap on your resume to explain, but don't make it the most important thing you mention there.
I hold what suggested earlier: Focus on including paid jobs that you've held for at least 6 months, and most importantly jobs that relate to the one you are applying. (As we usually say here "You should tailor your resume for the specific job you are applying to)."
Now, if this internship is not related to the job you will apply to, then I would suggest you follow my original advise and don't mention it.
Anyways, if a background check ever finds it you should be prepared to explain about this short experience you had.
Given all the details you mention I would suggest you don't put it on your resume.
It was a really short time (3 months), it was 3 years ago (plus the years that pass from today and the day you go back to India) and as you mention in comments you didn't learn much from it (if you include it and they ask about it during interviews what are you going to say why it was useful or what you learned?... Not much right...).
I suggest you include or focus on other experiences you have had. Try giving more importance to actual paid jobs you've had, ideally ones that you held for 6 months at the very least, and ones that you actually learned something and are related to the job you plan to seek.