"are there any US companies that hire only US citizens in India?"
If the day ever comes when this happens in India, I will personally leave my job here and picket outside such a company. Man, think about it, that will be the end of civilization.
Your US passport is not a medal you earned for which you can get a dollar salary while living in India. Nor is it a piece of property for which you can seek "rent". The passport doesn't really add any economic value to you from an employer's perspective, and I am surprised that you should even ask such a question.
I apologize if I sound harsh, but I am curious to know what is in your head.