Oral family history says that the family moved to Licking County, Ohio (Monroe Township area), may have lived in Iowa for a time and eventually settled in Illinois. Later descendants lived in Cook, Tazewell, Livingston and possibly McHenry and Hamilton Counties. The family is found residing in Johnstown Township, Licking County, Ohio in the US Census for 1840, 1850 and 1860. According to the Licking County Tax Records and Index - 1826 and 1834, prior to 1840 Joseph Barnum spelled his surname Barnham.
In the 1850 US Census for Johnstown, Licking County, Ohio the family of Joseph Barnum was enumerated as follows:
Dwelling #318; Family #322
Joseph Barnum, 53, M, Plasterer, Real property $800, b. Connecticut
Electa Barnum, 45, F, b. New York
Austin Barnum, 19, M, Blacksmith, b. Ohio
Timothy Barnum, 10, M, b. Ohio, Attended school within the year
Hellen Bassett, 14, F, b. Connecticut, Attended school within the year
A family tree on Ancestry.com shows Joseph's parents as Caleb Barnum (1765-1833) and Mary Boyd (1770-1797) but no source citation has been found to confirm that relationship.