I over paid child support and the counts say to refund the over payment but the State give the money to the mother and sayid sorry but they give my money away.
Can I get my over payment back?

If there's a court order to give you the excess money, then you should be able to get it back. The easiest way would be to adjust future payments owed. Is your child support paid via wage withholding? If so, then notify your employer of the court order and your employer can reduce the amount of wage withholding (or suspend it altogether) until the difference has been made up. If you make your payments yourself, then stop making payments until the amount you've overpaid has been covered.