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Visitation and Custody are two separate things.

As the only "known" natural parent you already have custody. An unmarried mother automatically has sole custody of a child, it's not something you have to go to court to get. After paternity is established he can file for visitation but until his paternity is established and visitation is granted, he has no rights to anything.

When paternity is established, that still does not take custody from you. You will still be the child's sole / primary custodial parent unless a court gives custody to him. It would take a whole lot of evidence that you are an abusive or neglectful parent before anyone could take your child from you. Even the child's father.

thanks for replies