"United States Census, 1850," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MHJF-NY8 : 12 April 2016), George W Madison in household of Caleb Madison, Clay, Hamilton, Indiana, United States; citing family 67, NARA microfilm publication M432 (Washington, D.C.: National Archives and Records Administration, n.d.).
As of the 1880 US Federal Census, he and Rhoda had nine children.
I don't have information on his parents, but in this census, his father's birthplace was listed as N. Carolina and Mom's birthplace was Ohio.
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It may be possible to confirm family relationships with George 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 George: