(a) A majority of the district judges in Nueces County may appoint an assignment clerk to serve under the presiding judge of the district courts in the setting and disposing of cases on the general docket. The assignment clerk shall perform the duties that are assigned to him by the district judges in connection with the setting and disposing of cases.
(b) The commissioners court shall set the salary of the assignment clerk and provide for the payment of the salary out of the general fund or the jury fund of the county. The salary shall be paid in monthly installments on vouchers approved by the presiding judge of the district courts.