The following data is extracted from Genealogy and Biography of Ontario County, New York.
(XIV) Jacob, son of Increase Carpenter, was born in Jamaica, in 1745, and married Widow Jane Smith, before her first marriage, Jane Baylis. She died May 6, 1813. He was a farmer by occupation and died in 1819 or 1820. Children, born in Jamaica: Increase, mentioned elsewhere: Jacob; Nathaniel; Daniel, married Hepsabeth Higbee; Benjamin, died about 1837; Deborah, married William Lewis; Catharine, married Alexander Jones.
Source: Genealogy and Biography of Ontario County, New York