(a) The judges of the probate court who by law are vested with the management of the county business and for whom no compensation is provided and the clerks of the superior courts, for public services in relation to which no compensation is provided by law, shall be compensated in accordance with this Code section.

(b) Such officers shall state their respective claims in writing and make an affidavit to the correctness and justice thereof. After the services are rendered, the claims so made out and verified shall be submitted to the grand juries of their respective counties at any regular term at which a grand jury is impaneled, provided that, if the statement is not submitted at that term or at the next succeeding term at which a grand jury is impaneled, such claim for services shall be barred. The grand juries may in their discretion require other proof of the justness and correctness of such claims and, when satisfied that the claims are just and correct, may allow the sum claimed or so much thereof as they may deem right and proper. When allowed, the judge of the probate court of the county or other authority levying county taxes shall assess so much with the other county taxes as will pay the same, which, when collected and paid over to the county treasurer of such county, shall be paid to the parties without further order, he taking a proper receipt therefor.

(c) The compensation provided for in this Code section shall be in full compensation of such officers for such services.