I've been caring for a friends little girl for 2 months. The mom is in jail and the grandmother has temp. Custody. I receive help the 1st month with food and now nothing at all they have only aske to see the little 2 times since I've had her and the grandmother who says she has ustody has ony called 3 times to check on her. Can I file for abondonment and who do I do that wit

No in Georgia abandonment has to do with the non custody parent not paying child support. Or leaving the child off at a store or something and driving off.

What you need to do is call social services or Child Protective services and have them come pick the child up.
Or just take the child back to the grandparent who has custody and give them the child back.

If you want to continue to care for this child then you need to talk to family services. Right now you have no legal standing to provide care for the child.