The process for this varies from State to State, with some offering far more help for overpaid child support than others. It can be as simple as asking the child protector for the return of over-payments, as they would have been the recipient of the checks. This, however, might fail, in which case the Child Support Agency for your local state should be contacted.
Because it is the local Child Support Agency that dictated the amount you were to pay each month, they should be the first port of call now you have realised you have been overpaying. In theory, the account with the CSA should state you have overpaid, as the extra amount might not have been paid to the mother. You are entitled to ask for the over-payments to be returned to you, however they might not agree to repay you, in which case you have two options: Sue the CP directly, or sue the CSA Department, who will in turn sue the CP. Whichever you choose you will need an attorney.
By suing the recipient, you would have to consider the cost of suing versus the chance of winning. If the dispute is taken to civil count over the small claims court, your expenses are increased markedly. Other things to consider here are whether your action would strain your relationship with the child, the most important party in this situation and whether the child support recipient is even legally obliged to pay you back.
Suing the Department would require requesting an administrative hearing on the over-payment. In this case, if the Department is made to pay you back they will likely take action against the recipient, which might again strain your relationship with the child.