Joseph may have been connected to Uriah Williams who is also found in the 1800 census for Morgan, Greene County, PA. He may also have been connected to Richard Williams found in the 1820 census for Morgan, Greene, PA.
1800 census 1 male 26-44, 1 male 45 and over, and 1 female 45 and over
Winter, G.L, "My Father's Family, Descendants of Richard Williams of Delaware, Pennsylvania, and Ohio," unpublished manuscript, 2012.
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