Ohio Rev. Code Ann. § 4963.39

If either party appeals from the judgment of a court in which an action under sections 4963.37 and 4963.38 of the Revised Code is begun, the party in whose favor judgment finally is rendered shall have included in his bill of costs against the adverse party, an attorney fee of fifty dollars, if it is not carried beyond the court of appeals. If carried to the supreme court, an attorney fee of one hundred dollars shall be included in his bill of costs.