Me and my daughter's father had my daughter out of wedlock in 2008 in Georgia. He was never supported her and has voluntarily disconnected all contact with me. I have tried several times to get in contact with him but he refuses to speak with me. We don't have court appointed child support order. My question is can I a child abandonment case against him and where do I go to file?

Since you haven't taken him to court then how would it be abandonment? Which is a criminal charge and it belongs in a different category.

In GA, they refer to failure to support a child as Child abandonment. It basically means a failure to provide support for a child. I believe such a charge can be bought after 6 months. But you can file support at any time after the child is born, so you should have filed for support immediately.

This site should help:
Georgia Family Law Blog: Frequently Asked Questions About Child Support

The biggest problem I see in how the law reads is adequate. There is no definition of it anywhere. Food clothing and shelter is all it says.

Is he on the birth certificate? That's the bigger issue right now because if he never signed it then he isn't even the legal father. You really need to go to court to get an order for support (that could have been done the day after the baby was born).