Legal Question in Family Law in North Carolina

You can not sign away parental rights sua sponte or on your own motion. The mother would need to seek to have your parental rights terminated. If that happens - you can agree to it or fight it. If your rights are terminated you do not have to pay child support. However, if your concern is that you are paying child support and the mother will not let you see the child without you kicking in a little extra cash - then you should consider going to court to force her to provide you reasonable visitation (assuming you are a suitable person to have visitation). From your description she is basically using the child to extort additional money from you.