Where there is no fence between property used for agricultural purposes and adjoining property of the state under control of the Department of Energy and Environmental Protection sufficient for the purposes of § 47-43, or when any fence so located is in need of replacement, and the boundary has been mutually agreed upon, the adjoining proprietor may, with the written agreement of the Commissioner of Energy and Environmental Protection, executed within sixty days of a written request by such proprietor, cause such a fence to be constructed or replaced within six months of the date of the agreement; and the commissioner shall, within sixty days after the construction or replacement is completed, reimburse the proprietor for one-half the cost thereof, the state’s share not to exceed four dollars a rod, payments to be made in the order of receipt of applications and completion of projects. Total payments under this section shall not exceed five thousand dollars in any fiscal year.