I am on birth certificate but never married mother can she keep son from me

As the biological father you do have rights. Are you a supportive father? Pay child support? Have part time custody? Written agreements? Lets go from these questions.

Unless she can prove you a danger to the child, she can't legally keep the child from you. But you have to enforce your rights. You need to go to court for joint custody and visitation.

In Georgia you an file for a visitation plan, even joint custody if you live close enough. But she can refuse to allow you to visit, until you get a court order.