If he didnt sign the birth certificate and the mother dosent want him to have anything todo with the child at all. If he were to give up his parental rights would he have to pay child support
That depends. The parents could come to whatever agreement they choose to with regard to dad's "rights", but technically speaking, child support is not waivable. You can set the support payment at zero, which eliminates the problem short -term, but leaves Dad on the hook later if the situation arises that Mom asks for it. Seek legal counsel in your area for more details. Good luck to you!