For serving any process, summons, or notice in a county other than the county of his residence, a sheriff shall charge 10¢ per mile for each mile traveled outside the county of his residence, whether the service is made by the sheriff or by a deputy. The fees shall be taxed as a part of the costs in the case to which the process, summons, or notice pertains. The sheriff, before serving or having served the process, summons, or notice outside the county of his residence, shall have a right to require the party or his attorney requesting the service to deposit with him a sufficient amount to cover the mileage fees provided for in this Code section.