If I sign my rights over does it cost something and can I do it for sure

The actual signing away of your rights doesn't cost anything ; just your signature on a piece of paper. But why would you want to? Unless it's to pave the way for someone else to adopt the child, you'll still have to pay child support. So there's really no practical reason for you to do so.

There are a lot of misconceptions about someone's ability to sign their rights away. Each state is different but usually in order to be allowed to do so you have to prove that you have completely abandoned that child for a certain number of years. What I mean by abandon is absolutely no contact whatsoever. Even then you may still owe child support but then it would just mean that you can't ever see the child. If your goal is to get out of child support, forget it, not going to happen even if you sign your rights away. If you have had any kind of contact with that child, you have to pay.