N.Y. Comp. Codes R. & Regs. tit. 18, § 301.2 – Definitions and conditions of eligibility for veteran assistance.

(a) Persons eligible or presumptively eligible for family assistance (FA) or in receipt of supplemental security income (SSI) are ineligible for veteran assistance.
(b) The child or grandchild living with the veteran and the dependent child of a deceased veteran means a person unmarried and under the age of 21 years. Child means a legitimate child, a stepchild, a legally adopted child, or an illegitimate child of the veteran acknowledged by the veteran or to whose support the veteran has been judicially ordered to contribute.
(c) Incapacitated children of a deceased veteran, who by reason of a physical or mental defect or infirmity are totally or partially disabled, are eligible for veteran assistance regardless of their age, if they are not eligible for FA or in receipt of SSI.
(d) The relationship of the wife, husband, child, grandchild, father, mother, step-father and step-mother to a veteran, and of the widow, dependent children or incapacitated children to a deceased veteran, shall be established by the usual investigation to determine eligibility for public assistance.
1. (1) Information thus obtained from the applicant and from documents in his possession, from members of his family, from legally responsible relatives and from other sources, which verify eligibility and degree of need, shall, under usual circumstances, be sufficient to establish the required relationship to the veteran or deceased veteran.
2. (2) If the investigation does not establish the required relationship to the veteran or deceased veteran and there is reasonable doubt as to the validity of the information, the sources of verification used in establishing relationship under similar circumstances in the FA program shall be consulted.
(e) Living with the veteran means living in the same household with the veteran, but includes also such situations where the veteran or his specified dependents are absent from the home under conditions that do not constitute the establishment of another or separate domicile.

A veteran and those related to him as defined and stated in sections 168 and 169 of Social Services Law are eligible for veteran assistance.