This family originated in England. A Goff branch of the YDNA family was in Maine via Canada by 1841. A Gough branch of the family migrated in the 1880s from England to Canada to Maine.
A descendant of George W. Goff b. 1841 Somerset Co., ME – 1913 Somerset, ME is a 36/37 match to the descendant of William Gough b. 1786 Worcestershire. George was seemingly orphaned by 1850 when he was living in Harmony, Somerset Co., ME with James Dodson b. ca. 1817 Ireland and wife Sophrona b. ca. 1825 Maine. In 1860, George W. Goff was living in Moscow, Somerset, ME with Peter and Mary Pierce. In the 1880 and 1900 censuses, he reported that his father and mother were b. in Ireland and Maine, respectively. It seems likely that he was referring to James and Sophrona Dodson when providing these places of birth.
A granddaughter of George W. Goff b. 1841 has atDNA matches to descendants of William Goff b. ca. 1781/1790 and Rebecca Bates. b. ca. 1775 ME, but the precise connection is unknown. While no YDNA evidence exists to show a connection, the family of Barzillai Goff b. 1800 ME son of William and Anna Goff also lived in Cumberland Co., ME.
William Gough, b. ca. 1786 Worcestershire, England, had a son William Gough b. ca. 1831 Kidderminster, Worcestershire. William Gough b. ca. 1831 was a puddler of iron, responsible for when molten pig iron was stirred in a furnace, in an oxidizing environment, resulting in wrought iron. He and his family migrated to Canada in the late 1880s and early 1890s, where some remained while others migrated to Cumberland Co., ME.
It is not clear if Goff and Gough branches settled in ME by coincidence or if there was awareness in the Gough family of Worcestershire of the Goff branch already being in ME.
The two participants (Goff and Gough) have taken YDNA111. Both should be upgraded to Big Y 700 to identify the generations to their shared ancestor.