Some of the important facts are not revealed in your post. Are you/were you married to the mother? If not, have you established legitimacy by court order? If not, you have no enforceable, legal parental rights. You need to file to establish legitimacy. It sounds like, but is not clear that the mother went to Texas some time ago (how long ago?) and left the child here in GA with you. Is that correct? You may have a reasonably strong claim to fight for primary physical custody, but that depends on many facts and circumstances not included here. You need to discuss all of the details with a family law attorney. Most of us provide free initial consultations over the telephone.
From a practical point of view, I ask you this, tell me why the judge should take the infant away from the mother. I will assume that no one is married in this situation. The first thing you will need to do is legitimate the child, then you can seek custody and visitation. You should assume that the mother will realistically stay in Texas. I will assume the reason she went to Texas is that she needs help with the baby and there are issues with your relationship with the mom. You need to speak with an attorney on this matter, as seeking custody/parenting time of an infant is not a do it yourself task. Additionally, before you file anything with the court should have an idea of how much you are going to pay in child support. Speak with an attorney as this will save you time and money.
I agree with Mr. Hopkins. If you are married to the mother, then you both have equal rights to the child. To get custody, you would have to file for divorce and the court would have to decide its in your child's best interest for you to have custody. If you are not married to the mother and have filed for legitimation, right now you have no rights to the child. You should file for legitimation and ask for custody. Again, the court will decide based on the best interest of the child. You should discuss your situation with an attorney who can advise you further based on more details than we have here. Do be aware, if she is in Texas for six months with the child and you have not filed a case in Georgia and there is no prior custody order in Georgia, then any custody case will have to be filed in Texas.
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