How do I file a damage suit against a person living in the US, who is spoiling my reputation and image?

If the state is not California, disregard this message, as I am a California lawyer but am not licensed to practice in any other state. If someone is spreading lies that harm your reputation, that is defamation either slander (spoken) or libel (written). You can sue for damage to your reputation and other damages. You need to identify the county in California where the defamer lives or works and sue in that county. You can find lawyers who handle defamation in that county by contacting that county's bar association. You don't need to be in California to sue in California, and you can even sue in your own name if you don't want a lawyer, but it will be best to hire a lawyer to handle the case for you. Be sure to give the lawyer all the written proof of the defamation you can get, and names and addresses of people who could testify about the defamation. Good luck.

Yes, you could file suit in that state against them and perhaps their employer if they work for one employer, but you would have to hire an attorney admitted to practice in that state and be able to prove what damages you suffer, which would be hard to do because at least some of the damage occurs in India so how are you going to get Indian witnesses to travel to America for any trial [even though most cases settle without a trial, the other side takes into account what you can prove at trial, so if they assume you can not produce any witnesses they would offer much less]. You need to speak to some attorneys in that state to see what they think about filing a suit or what you can do to prevent the defamation.