According to The Abridged Compendium of American Genealogy, Matthew (1737-1806) married in 1760 Jane Dibble, daughter of Lieutenant John.
The Barnum Family, 1517-1904 mistakenly calls him the third son of Thomas Barnum III (1696-1762) and Deborah Cornell. That Matthew was a different person.
According to the Genealogical & Family History of Southern New York, Matthew, son of Ephraim and Mehitable Barnum, was born in 1736 at Bethel, where he passed his life engaged in farming, and died in 1805. The valuation of his property in the grand list of 1793 was £75, 12s, 9p.
The Barnum Family gives his year of death erroneously as 1820.