N.Y. Civ. Serv. Law § 86
If the position in the non-competitive or in the labor class held by any honorably discharged veteran of the armed forces of the United States or by any veteran of the armed forces of the United States released under honorable circumstances from such service including (i) having a qualifying condition as defined in section one of the veterans' services law, and receiving a discharge other than bad conduct or dishonorable from such service, or (ii) being a discharged LGBT veteran, as defined in section one of the veterans' services law, and receiving a discharge other than bad conduct or dishonorable from such service, who served therein in time of war as defined in section eighty-five of this chapter, or by an exempt volunteer firefighter as defined in the general municipal law, shall become unnecessary or be abolished for reasons of economy or otherwise, the honorably discharged veteran or exempt volunteer firefighter holding such position shall not be discharged from the public service but shall be transferred to a similar position wherein a vacancy exists, and shall receive the same compensation therein. It is hereby made the duty of all persons clothed with the power of appointment to make such transfer effective. The right to transfer herein conferred shall continue for a period of one year following the date of abolition of the position, and may be exercised only where a vacancy exists in an appropriate position to which transfer may be made at the time of demand for transfer. Where the positions of more than one such veteran or exempt volunteer firefighter are abolished and a lesser number of vacancies in similar positions exist to which transfer may be made, the veterans or exempt volunteer firefighters whose positions are abolished shall be entitled to transfer to such vacancies in the order of their original appointment in the service. Nothing in this section shall be construed to apply to the position of private secretary, cashier or deputy of any official or department. This section shall have no application to persons encompassed by section eighty-a of this chapter.
N.Y. Civ. Serv. Law § 86