If the father and Mother never married but the father does pay child support and his name is on the birth certificate and she is refusing visitation what are his rights?

He can, and should, file a petition with the Court to grant him visitation. Regardless of paying child support, he has the right to see his child unless he is deemed to be a danger to the child (sex offender, drug charges, violent crimes etc). If he is low income - usually double the poverty rate, so under abount $20,000 a year - your state's legal aid services can help him file for free or a few hundred dollars, income dependent. Google legal aid for your state. If not low income, get an attorney and have him/her ask, in the petition for visitation, that the mother pay the attorney fees and court costs. This is a no brainer and visitation will be granted (unless the danger factor is present - in which case don't bother filing until you clean up you life.)