I have a 7 year old son. I was 16 when I got pregnant and the father 18. He is not a part of his life. He is orderd to pay child support but doesn't. Does this man have any rights to my child if so what can I do to terminate them? Please help I'm so confused.

He has rights but he would have to go to court and file for partial custody/visitations. Why don't you go back to court and tell them he is not paying his child support?
Also support and custody are two different issues. Many moms think they can with hold visitations because he isn't paying but that is not the way it works... just for future reference.

Assuming he has been declared the legal father (either by being on the birth certificate or being so declared in court), then he has the same rights as any father.

Whether he exercizes those rights is another matter.

Courts are VERY reluctant to terminate rights. Generally they will only do so to clear the way for an adoption or if the parent represents a danger to the child.

If he isn't a part of your child's life, then why not just leave things alone? Or why haven't you pursued support?