Otsego County is only entitled to payment to the extent that they filed a support petition against you and the mother. Did they do that? As for recouping support payments from the mother, the date you fike the petition terminating your obligation, is the retroactivity date for recoupment purposes. You could commence a civil action attempting to recoup overpayments, but you won't get recoupment from family court.
You will need to sue, and it can be brought in small claims court so you will need need to spend a lot of money fighting the action. It is worth a shot.