In addition to the state tax and fee imposed by §§ 58.1-1712 and 58.1-1717.1, the governing body of any county and the council of any city may, as provided in § 58.1-3805, (i) impose a county or city tax in an amount equal to one-third of the amount of the state tax on the probate of a will or grant of administration on the probate of every such will or grant of administration and (ii) charge a $25 fee for the recordation of a list of heirs pursuant to § 64.2-509 or an affidavit pursuant to § 64.2-510, as provided in § 58.1-1717.1.