I am a single mother who thought my boyfriend was the father of my child. Now another ex has surfaced claiming he is the father and has asked the court for custody of my child. He has a restraining order and has made countless false allegations against me. He has had no contact with my child except for a few meetings to threaten me and accuse me of not letting him see the child. I did see a lawyer who filed papers requiring him to have supervised visits which he has not followed through with. Now he is suing for custody? What should I do?

You go through with the DNA test to hopefully prove he is not the father. If he is not then he doesn't have a leg to stand on.

Why are you (and a lawyer for sure) agreeing to supervised or any visits, without a DNA test.

You require a DNA test to prove who the father is, Start with the boyfriend you think it is, and see if he is really the father, that would shut down any court action

But respond to his court request with a request for court ordered DNA test.

Next, for him to get custody, he will have to prove you an unfit mother, with proof in court, not claims that can not be proved

... I did see a lawyer who filed papers requiring him to have supervised visits which he has not followed through with. ...

The papers wouldn't require him to have visitation, supervised or otherwise. They would allow visitation.

And if he can establish paternity, he should be required to pay you child support.

I think she meant supervision is required. Did you do a DNA test?