You can have an "Armed Forces" designation printed on your Ohio driver license or state ID card as proof of military service. Adding the designation itself is free, though the normal fee still applies for a first issuance, a renewal or a duplicate credential.
Apply in person at an Ohio Deputy Registrar License Agency, or online or by mail depending on your military status. For more information, use the Ohio Department of Public Safety guidance for online and mail-in applications.
Your current Ohio driver license or ID card plus one of the following: your DD214, an active or retired military ID, a Veteran ID card, or a copy of your current orders.