(a) Each family support magistrate who ceases or has ceased to hold office because of retirement other than under the provisions of § 5-169 or 51-49 and who is an elector and a resident of this state shall be a family support referee for the remainder of his term of office as a family support magistrate and shall be eligible for appointment as a family support referee during the remainder of his life in the manner prescribed by law for the appointment of a family support magistrate. Each such family support referee shall exercise the powers of a family support magistrate.

(b) (1) On and after July 1, 2021, each family support referee shall receive, for acting as a family support referee, in addition to the retirement salary, the sum of two hundred thirty-three dollars and expenses, including mileage, for each day a family support referee is so engaged.

(2) On and after July 1, 2022, each family support referee shall receive, for acting as a family support referee, in addition to the retirement salary, the sum of two hundred forty-five dollars and expenses, including mileage, for each day a family support referee is so engaged.