This family originated in what is now the United States, likely in SC another southeastern state.
William G. Goff was born ca. 1855/1857 SC and died 1909 Emanuel Co., GA. He lived in Emanuel Co., GA starting in 1880 where he had six children by three women. Curiously, descendants of William G. Goff of Emanuel Co., GA have significant atDNA matches to descendants of William Gauf of Richland Co., SC, who had a wife and two daughters. The two Williams were concluded to be identical, based on strong atDNA and XDNA matching. When William Gauf moved to Emanuel Co., GA in 1880, he left behind his wife and two daughters.
A combination of YDNA, Big Y 700 and atDNA results, points to William G. Goff being descended from a Carter male born in the 18th century who adopted the Goff surname. The simplest explanation is that a Goff female had male child by a Carter male and gave her son the Goff surname.
The analysis would benefit from expanded atDNA testing at different labs to identify the generations that elapsed between the Carter/Goff male child and William G. Goff.