You need to speak with a good attorney to file a petition for custody and to relocate to GA ASAP! You might want to go to the police in the meantime as he is not the legal father and is withholding the child wrongfully under any interpretation.
I agree with Mr. Trabin's comment and Ms. Jacobs' answer in that the biological father currently has no rights to the child. If you're going to move to Atlanta, there is nothing to stop you so long as you do it before he starts any legal proceedings to establish his Paternity and ensuing rights.
This response is for general purposes only and does not establish an attorney-client relationship. You should contact an attorney to fully discuss your issues.