(a) An appointment by the county clerk of a deputy clerk must be in writing, be signed by the county clerk, and bear the seal of the county court. The county clerk shall record the appointment in the county clerk's office and shall deposit it in the office of the district clerk.
(b) A deputy clerk must take the official oath.
(c) A deputy clerk acts in the name of the county clerk and may perform all official acts that the county clerk may perform.