In 1850, he was in Trigg County Kentucky and is listed as the head of household for a family that included Mary (probably his wife), John, William and Elizabeth.
The 1860 Census has his wife Nancy Miller listed as a widow. This means he died sometime between 1853 and 1860.
Just for reference, here's a bit of lore from the family: William was married to "Mary", (There are conflicting reports of her full name. It is either Mary Catherine Trizzell or Mary Antawoneese Woody). Mary was half Cherokee. The family was split up in Kentucky with an infant child and Mary forced on westward to Indian territory, and Elizabeth and her older siblings staying with their father in Kentucky.
Sources
Census Record(s):
1850 US Federal Census: Kentucky, Trigg County, District 2; Family 595, Lines 25-29; William Miller, Head of Household
"United States Census, 1850," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:M65L-TN3 : 4 April 2020), William Miller, Trigg county, Trigg, Kentucky, United States; citing family 595, NARA microfilm publication M432 (Washington, D.C.: National Archives and Records Administration, n.d.).
Marriage to Nancy Mayes:
"Kentucky, County Marriages, 1797-1954," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:QKJ9-PX9V : 17 May 2018), William Miller and Nancy Joyce, 11 Aug 1853; citing Marriage, Trigg, Kentucky, United States, various county clerks and county courts, Kentucky; FHL microfilm 321,335.
"Kentucky Death Records, 1911-1965," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:N96V-H9X : 9 January 2019), William Miller in entry for George Washington Miller, 1945; citing Death, Kentucky, United States, certificate , Office of Vital Statistics, Frankfort; FHL microfilm 2,073,565.
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DNA Connections
It may be possible to confirm family relationships with William 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 William: