If the money has been distributed to your ex-, the state does not have the money to refund to you.
If the issue of a credit was not addressed in the prior order, and the administrative agency won't give you a credit without further order of the court, then you will need to obtain a clarification from the court. That may not be a refund; for example, it could be an order that your ongoing support be reduced by a certain number of dollars until the overpayment is satisfied, or a credit to be applied to your final months of support before the support obligation expires. That will depend upon factors including the full facts and context, the amount, and the policies of the court, as well as any statutory restrictions that may apply.

