"United States Census, 1930," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:3N5B-8T2 : accessed 28 June 2018), Vermont W Robinson in household of William M Robinson, Fairfield, Jefferson, Alabama, United States; citing enumeration district (ED) ED 205, sheet 4B, line 82, family 61, NARA microfilm publication T626 (Washington D.C.: National Archives and Records Administration, 2002), roll 33; FHL microfilm 2,339,768.
"United States Census, 1940," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:V1G2-19B : accessed 28 June 2018), Vermont Robinson in household of W M Robinson, Election Precinct 7, Jefferson, Alabama, United States; citing enumeration district (ED) 37-31, sheet 1B, line 65, family 20, Sixteenth Census of the United States, 1940, NARA digital publication T627. Records of the Bureau of the Census, 1790 - 2007, RG 29. Washington, D.C.: National Archives and Records Administration, 2012, roll 43.
"Alabama Deaths, 1908-1974," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:JXFY-N4J : 15 February 2018), William Vermont Robinson, 16 Mar 1966; citing reference 6584, Department of Health, Montgomery; FHL microfilm 1,909,088.
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: