2023 New York Laws
ACG - Alternative County Government
Article 4 - County Executive
156 - Deputy County Executive.

§ 156. Deputy county executive. 1. The board of supervisors shall have
  power  to  authorize  the county executive to appoint one or more deputy
  county executives. Every appointment of a deputy county executive  shall
  be  in writing filed and recorded in the office of the county clerk. Any
  such appointment may be revoked by the county executive at any  time  by
  filing a written revocation in the office of the county clerk.
2.  A  deputy county executive shall perform such duties pertaining to
  the office as may be directed by the county executive.
3. The deputy designated by the county executive for the purpose shall
  have the powers and perform the duties of the  county  executive  during
  his absence or disability.
4.  If  more  than one deputy county executive shall be appointed, the
  county executive shall designate in writing and file in  the  office  of
  the  county  clerk  and  clerk  of the board of supervisors the order in
  which such deputies shall exercise the powers and duties of  the  office
  in  the  event  of  the absence or inability of such county executive to
  perform the duties of the office.
5. The head of any department may be designated  to  serve  as  deputy
  county  executive but without additional compensation. In the event that
  no deputy county executive has been appointed or designated, or  in  the
  event  that  the  deputy  appointed or person so designated is unable to
  serve, the board of supervisors shall designate the head of a department
  or other qualified person to perform the duties of the office during the
  absence or inability of the county executive.