Can I file a child abandonment case to modify child support,on my child's father. He is doing anything and all he can to not support the child. Also I have no way to contact him. But when I tried to contact him his live in girlfriend interferes and he lets her.

Unless you are in Georgia, then you don't file an abandonment case. If you want a modification of support you file for a modification. However, there has to be a change of circumstances for the court to grant one.

You an go back to court to have the court enforce the current support order you have.