Ohio Rev. Code § 3119.966: Costs and attorney fees.

(A) If relief from a child support order is not granted pursuant to section 3119.962 of the Revised Code, the court shall require the person who filed the motion for relief to pay all court costs of the action and the reasonable attorney's fees of the opposing party.

(B) If a person files an action under Chapter 3111. of the Revised Code as described in section 3119.965 of the Revised Code and the court determines that no parent-child relationship exists between the person or the male minor and the child, the court shall require the person who filed the action to pay all court costs of the action and the reasonable attorney's fees of the opposing party.