The Barnum Family, 1350-1907 calls him Azoe Barnum; The Barnum Family, 1517-1904 says he had 6 sons and one daughter. A Genealogy of Benjamin Cleveland agrees that he left a widow and seven children upon his death, not mentioning John Azor Barnum as one of them. The John Azor Barnum listed as Azor's son in the Genealogical Record of the Barnum Family, is almost certainly his grandson by his son Clarence Adalbert Barnum.
In the 1850 US Census for Junius, Seneca County, New York the family of Azor Barnum was enumerated as follows:
Dwelling #1326; Family #1417
Azor Barnum, 36; M; Farmer; b. New York
Louisa Barnum, 33, F, b. New York
G. B. Barnum, 11, M, b. New York, Attended school within the year
N. F. Barnum, 4, M, b. New York
A. L. Barnum, 2, F, b. New York