Ohio Rev. Code § 141.07
In addition to the annual salary and expenses provided for in sections 141.04 and 141.05 of the Revised Code, each judge of the probate court, and of the juvenile court, while holding court in a county in which the judge does not reside, by assignment of the chief justice of the supreme court under section 2101.37, 2101.39, or 2151.07 of the Revised Code, and each judge of the common pleas court while holding court in a county in which the judge does not reside, by assignment of the chief justice of the supreme court under section 2701.03 of the Revised Code, or without any assignment, shall receive the actual and necessary expenses that the judge incurred while so holding court in that county, to be paid from the treasury of that county upon the warrant of the county auditor. Each judge of the court of common pleas, of the probate court, and of the juvenile court, who is assigned by the chief justice by virtue of section 2503.04 of the Revised Code, each judge of the probate court who is assigned by the chief justice by virtue of sections 2101.37 and 2101.39 of the Revised Code, and each judge of the juvenile court who is assigned by the chief justice by virtue of section 2151.07 of the Revised Code, to aid in disposing of business of some county other than that in which the judge resides shall receive fifty dollars for each day of the assignment and the actual and necessary expenses that the judge incurred in holding court under the assignment, together with the judge's actual transportation expenses, to be paid from the treasury of the county to which the judge is so assigned upon the warrant of the auditor of that county.
R.C. §141.07