Note: The stone is a bit difficult to read so the death date might be off. The date of death has to be after 1830 (so his Findagrave memorial is wrong - it lists his DOD as 1813), since the 1830 census shows him still alive.
This is James' household in the 1830 US Census - he had to be at least 50 years old.
Name James Wilkin, Home in 1830 (City, County, State)Orange, New York.
Total - All Persons (Free White, Slaves, Free Colored) - 5 
↑ Year: 1830; Census Place: Cornwall, Orange, New York; Series: M19; Roll: 113; Page: 204; Family History Library Film: 0017173. Description: Township: Cornwall. Source Information: Ancestry.com. 1830 United States Federal Census [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2010. Images reproduced by FamilySearch. Original data:Fifth Census of the United States, 1830. (NARA microfilm publication M19, 201 rolls). Records of the Bureau of the Census, Record Group 29. National Archives, Washington, D.C.
Will and probate: Item Description: Letters of Administration, Vol F-G, 1827-1846. Probate Records, 1787-1916 ; Index to Surrogate's Records, 1787-1941; Author: New York. Surrogate's Court (Orange County); Probate Place: Orange, New York. Ancestry.com. New York, U.S., Wills and Probate Records, 1659-1999 [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2015. Original data: New York County, District and Probate Courts. Name: James A Wilkins, Probate Date: 5 Jul 1842, Probate Place: Orange, New York, USA, Inferred Death Year: Abt 1842. Inferred Death Place: New York, USA.
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It may be possible to confirm family relationships with James by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
However, there are no known yDNA or mtDNA test-takers in his direct paternal or maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with James: