(F) For any county that accepts the payment of dog and kennel registration fees by financial transaction devices in accordance with section 955.013 of the Revised Code, in addition to those registration fees, the county auditor shall collect for each registration paid by a financial transaction device one of the following:

1. (1) An administrative fee of seventy-five cents or another amount necessary to cover actual costs designated by the county auditor;
2. (2) If the board of county commissioners adopts a surcharge or convenience fee for making payments by a financial transaction device under division (E) of section 301.28 of the Revised Code, that surcharge or convenience fee;
3. (3) If the county auditor contracts with a third party to provide services to enable registration via the internet as provided in section 955.013 of the Revised Code, a surcharge or convenience fee as agreed to between that third party and the county for those internet registration services. Any additional expenses incurred by the county auditor that result from a contract with a third party as provided in this section and section 955.013 of the Revised Code and that are not covered by a surcharge or convenience fee shall be paid out of the allowance provided to the county auditor under section 955.20 of the Revised Code.