Georgia does recognize the mother as having sole physical and legal custody by operation of law for children born in wedlock, leaving the burden to putative father to file a petition for legitimation. You need to go to the court and file this with the court clerk. During this process, the father can request to seek visitation and/or custody. He may even file to change the childs last name if necessary, keeping in mind that they law is there for the benefit of the child.
It's during this process that the mother will be served with the process of the petition and given an opportunity to object this claim, however, once the paternity is "established", the father may file another court action seeking custody.
Once a case is active, you can utilize many programs in Georgia for help in this process through the Office of Child Support Services (OCSS) such as family mediation, etc. If at all possible, finding legal representation is always suggested. If you cannot afford one, here are some self-help legal resources in Georgia.
http://www.fultonfamilydivision.com/ (Fulton County-Superior Court Family Division's Family Law
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