Can the father of my kid get any rights to him if he has never paid for anything or stopped seeing him for over six months?

Yes.

State laws vary, but generally, if he has not been found an unfit father, he has visitation rights until the court revokes them.

Have you went to court and got court ordered child support ?

If that answer is NO< then he does not even owe anything, he will start to owe you support after you get a court order for support.

Next he can file for visits anytime he wants, he does not lose his rights over this.