In the 1850 US Census for Bristol, Ontario County, New York is enumerated the family of a Jabez Barnham who might be this individual, as follows:
Dwelling #35; Family #36
Jabez Barnham, 46, M, Mason, Real property $300, b. New York
Joanna Barnham, 39, F, b. New York
Elisabeth Barnham, 16, F, b. New York, Attended school within the year
Theodora Barnham, 12, F, b. New York, Attended school within the year
Ann Barnham, 9, F, b. New York, Attended school within the year