The part of the question that is missing is: "to whom are you going to sign over rights?" Georgia law will not allow on parent to simply sign over (or waive) their rights as a parent, because taht would go along with a waiver of that parent's obligations to the child. The idea is that a child is entitled to two parents, and those parents have obligations to that child.
IF there is somebody willing to step in for you (as in an adoption) THEN you could sign your rights over to him... But it sounds like you want to do this unilaterally, and that is simply not allowed. The only thing you could do would be to wiave your "rights" while you would have to keep your "obligations".
Best of luck,
You are not going to be allowed to release your parental rights unless someone is going to adopt the child. Your child support is your responsibility, no one else's. Also, there is the public policy against creating legal bastards, which is what you would be trying to do. Exercise your visitation; if its being denied go to court.
Parents do not have the ability to "sign over rights" in the sense of giving up all rights and obligations to a child unless it is to allow someone to adopt the child. Your rights could otherwise be terminated in a deprivation action if the court found that it would be in the best interest of the child. But to relieve you of a support obligation would certainly not be grounds for such a termination.
I would suggest you consider taking the necessary steps to develop your bond with your child. You would likely find it very rewarding and so would the child. If the mother is difficult about it get an attorney and get your rights established by the courts.