What is the name of your state (only U.S. law)? Georgia
When parents are not married, who has legal custody of the child? Where can I find the legal document that states this is a law?
In cases where there is no establishment of paternity, the Mother (the ONLY parent) is presumed to have custody of the child.
In cases where paternity is established, and the child has two legal parents, some states assume that both parents have equal rights to the child.
Georgia is not one of those states. Georgia requires that the presumed father establish paternity AND go through a legitimization process prior to even having standing to sue for custody.
http://www.georgialegalaid.org/files/6FCBD72D-B465-109D-9EC1-5A4F52A74EE9/attachments/A90A1C4F-A820-5A24-567C-618EFC34C418/92041GLSP%20Child%20Custody%20in%20GA%20-%2007-07.pdf
Google is your friend.