My response:
From my research of the issue, Ohio law now requires you to file a motion to transfer in the county where the original judgment, court order or child support order was made. It will allow you to file a motion to transfer the action to your own county if you can show it would be a hardship for you to have the child support administered from the county where the original orders and procedure took place.
Ask the clerk of the court in the old county if there are any forms concerning transfer of child support to your new county. Also, inquire about filing fees.
Good luck.
IAAL