The Barnum Family calls him Theodore Poin Barnum, and notes his two marriages but says he had no issue.
In the 1850 US Census for Burns, Shiawassee County, Michigan the family of Theodore P. Barnum was enumerated as follows;
Dwelling #35; Family #35
Theodore Barnum, 38, M, Wagonmaker, Real property $400, b. New York
Elizabeth Barnum, 36, F, b. Connecticut
John E. Barnum, 3, M, b. Indiana
Sylvanus Stilson, 15, M, Wagonmaker, b. Ohio, Attended school within the year
James Sleath, 26, M, Physician allopathy, b. Scotland
'The Barnum Family, 1517-1904' gives an incorrect death year of 1836.