FamilySearch.org profile: William T Varney; free-use site, login required to view profile and source documents; profile created through membership collaboration; date accessed: 2 Nov 2018
"United States Census, 1900," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:M9HP-5RT : accessed 3 November 2018), Willi Varue in household of Sleury Varue, Magisterial District 6, Big Creek, Pike, Kentucky, United States; citing enumeration district (ED) 85, sheet 2B, family 32, NARA microfilm publication T623 (Washington, D.C.: National Archives and Records Administration, 1972.); FHL microfilm 1,240,548. (presumed match)
"United States Census, 1910," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:M26B-TZX : accessed 3 November 2018), William T Varney in household of Henry Varney, Big Creek, Pike, Kentucky, United States; citing enumeration district (ED) ED 178, sheet 3B, family 49, NARA microfilm publication T624 (Washington D.C.: National Archives and Records Administration, 1982), roll 499; FHL microfilm 1,374,512.
It may be possible to confirm family relationships with William by comparing test results with other carriers of his ancestors' Y-chromosome or 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 William: