Her father is very unstable mentally and does not think of anyone beside his self. He wants to sign off rights so he does not have to pay child support anymore and I would be more than happy to let him so that way my daughter and I don't have to deal with him problems any more. Is this allowed in Ohio and if so how can I go about doing this? If not is there anything else I can since he has never hurt my daughter but my daughter hates to go see him so are court order is he gets her every other weekend but I have not made her go and have put her into counseling to help with her axnitey about her father. I have tired to talk with him one on one but he thinks just because I make better money than him than he should get his child support back and when I don't do it and tell him if he does not like it he needs to have it changed in the courts. He than calls me a *****, ****, and anything else and says things like if you does this you will regret this and I will make you pay. Anything I can do about is all done over the phone and I have no proof to prove it?

First, no you can't get him to sign over his rights. Only a court can terminate parental rights and courts are very reluctant to do so. There is a sticky at the top of this forum that explains this:
https://www.askmehelpdesk.com/family-law/signing-over-rights-read-first-116098.html

If he has court ordered visitation you cannot stop it. On the other hand you cannot force her to go. You have to make her available for his scheduled visitation but you don't have to physically force her to go with him. If you don't make her available, you could be cited for contempt of court.

If she is balking, then you get her counseling and go back to court to request that visitation be curtailed, or made supervised or ended. You get her counselor to testify what is in her best interests.