Ohio Rev. Code Ann. § 3127.44

An appeal may be taken from a final order in a proceeding under sections 3127.31 to 3127.47 of the Revised Code. The supreme court of this state shall, by rule, provide for expedited appellate review of cases appealed under this section. Unless the court enters a temporary emergency order under section 3127.18 of the Revised Code, the enforcing court may not stay an order enforcing a child custody determination pending appeal.