This family originated in the United States, most likely in SC or Tennessee.
Two descendants of Thomas H. Goff b. 1858 TN through his sons William Madison Goff b 1892 KY and Homer Thomas Goff b. 1901 AR were confirmed as having a shared paternal ancestry by YSNP matching. Thomas H. Goff was a son of James Madison Goff b. 1826 TN. The William Madison Goff descendant has taken a YDNA111 test, which was used to estimate his haplogroup as I-P109. The Homer Thomas Goff descendant took an AncestryDNA test, from which YSNPs were extracted. The extracted YSNP path led to I-P109. On the strength of shared surname, geography and YSNP, this genetic family is proven.
The founder of this family was Nancy Goff b 1810 SC. Nancy had two sons, James Madison Goff and Frank Goff, who was the father of James Monroe Goff b. 1857 TN. A descendant of James Madison Goff has taken a YDNA test and does not match the two descendants of James Monroe Goff.
YDNA testing of additional descendants of James Madison Goff will help sort out the early generations of this family. One possibility is that Nancy Goff had her sons James Madison Goff and Frank Goff by different men.