(a) The council of any incorporated town shall have power to provide, by ordinance, for the election of a town marshal and such other subordinate officers as they may think necessary for the good government of the town.
(b) In regard to the officers mentioned in subsection (a) of this section, the council shall have the power to:
(1) Prescribe their duties and compensation or the fees they shall be entitled to receive for their services; and
(2) Require of them an oath of office and bond with surety for the faithful discharge of their duty.
(c) The period for the election of any officer shall be fixed at the time of the regular biennial election. No appointment of any officer shall endure beyond the period of the term of office of the council making the appointment and one (1) week after the qualification of the members of the succeeding council.