My daughter's father pays child support, but his name is not on the birth certificate. He signed a paternity agreement when she was born in order to pay child support. What rights does he have to see her? He has made no effort to see her in 5 years and now wants to come and see her. I don't trust him alone with her. What legal rights does he have?

If he is the father, and the agreement you made and signed with him is evidence that he is, he has as much right to custody of and visitation with the child as you do; absent a court order.

What is it you don't trust, he may abuse the child ? Run off with the child.

But he signed paternity and this is legally binding to show him as the father, the court accepted this to establish child support.

What you never did was to get legal custody of the child I will assume nor did he get a court order for visits.

Does he have rights to visit, yes, if you don't allow it, he can go to court and get a court ordered visits.
If there is danger you ask in court for supervised visits and present your evidence

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but he signed paternity and this is legally binding to show him as the father, the court accepted this to establish child support.
...

But the question is whether it's legally binding on the mother (OP). If she signed it too (and I have assumed that she did), it probably would be. If the agreement was with the state child support agency (and if welfare was involved), it might be a closer question.