Custody was awarded to the father approximately 9 months ago. He has failed to come pick the child up he has just used the court papers to stop child support. We live in two different states his home state awarded him custody. My child has been in my care in my home state for the last 3 1/2 years neglect or abuse is not an issue. Children and Family Services were not involved but there was a GAL assigned who felt that the father would be the parent to most likely facilitate visitation. The father's mother has worked for the Juvenile Court system in their state for over 20 years and in the end the father was awarded custody. Since stopping his support payments he has provided absolutely no support for my child. He calls my child about 3-4 times a month but that is the extent of his parental involvement. Just recently there was a support hearing held in his state and they are now seeking support payments from me for a child that has been in my care the entire time. Could this behavior be considered Child Abandonment? Can I take out a Child Abandonment Warrant on him and ask for emergency custody in my state? What are my options?

No you can't file for a child abandonment warrant. Or anything to do with child abandonment really. What you can do is contact the court that awarded him custody because they have jurisdiction. Let them know that you have proof that the child has been with you the eitire time. If you don't get any answers get a lawyer and file in your state for a change in jurisdiction based on the fact that they haven't lived in that state for three years. If the change is granted then you can petition the court for custody and child support but you really need to get a lawyer especially because you have waited this long to do anything.

No, he has not left the child setting in walmart alone,

He is merely not using his rights to visit, and not paying child support. You can can and should turn him over to child support enforcement, Ga has a great one.
This is not abandoment in GA, and never will be if he does not visit or pay for 10 years