Hello

Yes, your son has chances of getting a medical seat in Government Medical Colleges of Tamil Nadu with a score of 385 marks, BC category, and under state quota; if we keep last year's cutoff in consideration.

You can go through the list of government medical colleges and their last year's cutoff to get a much better view of your credibility to get a medical seat, with the help of the link mentioned below- 

https://medicine.careers360.com/articles/neet-cutoff-tamil-nadu

I hope this information proves helpful to you.

All The Best