Abraham / Abram was born abt 1836 in New York. His parents were Samuel Avery and Mariah. 
1850 lived with father in Phillipstown, Putnam, New York 
Samuel Avery Male 52 Vermont
Electa Avery Female 23 New York
Ann Avery Female 21 New York
Ellen Avery Female 18 New York
Hannah Avery Female 16 New York
Abram Avery Male 14 New York
Edward Avery Male 9 New York
Jacob Van Voorhes Male 23 New York
Samuel Avery Male 17 New York
Abram Avery, age 24, married H. F. (Henrietta Frances) Beasley, age 21, Jan 18 / 19 1860 in Charlotte, Virginia. Her parents were Jordan R / W Beasley and Judith. She was born in Halifax County, Virginia. 
1860 lived with father and Henrietta in Phillipstown, Putnam, New York 
Samuel Avery Male 60 New York
Electa Avery Female 30 New York
Abraham Avery Male 24 New York
Edward Avery Male 20 New York
Henrietta Avery Female 21 Virginia
1870 Abram and Henrette lived in Philipstown, Putnam, New York 
Abram Avery Male 35 New York
Jane Avery Female 30 New York << change submitted to Henrietta, born in Virginia
Samuel Avery Male 9 New York
Anna Avery Female 7 New York
Ida Avery Female 5 New York
Henry Avery Male 3 New York
Belle Avery Female 0 New York
Beverly Avery Male 0 New York
1880 Abram and Henrette lived in Philipstown, Putnam, New York 
Abram Avery Self Male 44 New York, United States
Henrette Avery Wife Female 40 Virginia, United States
Samuel Avery Son Male 19 New York, United States
Henry Avery Son Male 14 New York, United States
Belle Avery Daughter Female 9 New York, United States
Sylvester Avery Son Male 8 New York, United States
Emma Avery Daughter Female 6 New York, United States
John E Avery Son Male 4 New York, United States
1870 census image shows Abram's 'wife' as Jane, not Henrietta, but since they married in 1860 and she is in 1860 and 1880 census with Abram with same children as 1870 census, the 1870 Census name and birth location is incorrect. Correction has been submitted to family search Oct 2020 for her name and birthplace for 1870 census.
Henrietta is listed as mother of children listed in 1870 census, also.
↑ United States Census, 1850," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MC1W-PYW : 9 November 2014), Abram Avery in household of Samuel Avery, Phillipstown, Putnam, New York, United States; citing family 117, NARA microfilm publication M432 (Washington, D.C.: National Archives and Records Administration, n.d.).
↑ "United States Census, 1880," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MZFQ-JQ3 : 8 September 2017), Abram Avery, Philipstown, Putnam, New York, United States; citing enumeration district ED 79, sheet 73B, NARA microfilm publication T9 (Washington, D.C.: National Archives and Records Administration, n.d.), FHL microfilm 1,254,917.
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It may be possible to confirm family relationships with Abram 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 DNA with Abram: