Child Legitimacy help

My boyfriend just found out he has a little boy by a girl he dated before me. The baby was born in Wisconsin but the baby and mother now live in Georgia. We had an at home paternity test performed on the baby and it is in fact my boyfriend's son. She was upset that he wouldn't date her anymore and is now refusing to let him see the baby and has actually attempted to give him away to strangers instead of giving him to us. I know Ga law says that he is not legitimate because my boyfriend did not sign the legitimacy papers in the hospital plus the baby is in another man's last name. We want him in our lives especially if she is going to give him away to strangers but we are unsure if we need to file legitimacy papers here in Ga as the game law says we should since they now live in Ga or if we have to petition the state in which he was born. Please advise me on the correct procedure.