The following data is extracted from Genealogy and Biography of Ontario County, New York.
Arthur Williams, immigrant, was born in England and settled in Windsor, Connecticut, as early as 1640, removing thence to Northampton, Massachusetts, in 1659. He married, November 30, 1647, Catherine Carter, widow of Joshua Carter, of Windsor, and she married (third) February I1, 1677, William Branch, of Springfield. She died August 8, 1683. The only child of Arthur and Catherine Williams was Zebediah, mentioned elsewhere.
Source: Genealogy and Biography of Ontario County, New York