Individual Details

There is evidence that his parents were Betsy Morgan and Andrew Farrell. Betsy's husband, Joseph Branham, died before 1850. Andrew was close to the Branham and Morgan families ( Andrew was son of James 3rd wife Elizabeth Herdon Ferrell).
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From 4Jansfamily4's Branham Family Tree in Ancestry:

Malissa Woodard Hall (dau of John Randolph Ferrell) told Lucille (dau of Nora Hall-dau of Eliza Farrell and Alexander Hall) that she, Melissa Hall, was the granddaughter of Melissa Damarel and Andrew Jackson Ferrell. And that Eliza Ferrell Hall's grandmother, Eliza (Herdon) Ferrell had run away with an Indian. Her parents got her back but she was pregnant with the Indian's baby whom she gave birth to and kept, naming him Andrew Jackson Ferrell.
ca 1827 Eliza Herdon married Andrew Farrel.
1827-28 Eliza left her husband to live with Iroquois Indian over mountain into Ohio.
1828 - Eliza returned to Russell Co, VA pregnant with baby
1828 - Eliza gives birth to Iroquois baby, Andrew Jackson Ferrell. Eliza and Andrew Ferrell then have three ch together -Wm J, Sophia and Randall.
1839 - Eliza married James Morgan (father of Elizabeth Betsy Morgan Branham who had married Joseph Branham 1834.
1850 Larkin Herdon leaves $50 each to Wm J and Sophia Ferrell in his will (obviously had disowned daughter, Eliza).
1850 - Wm Jennings Branham is born to Betsy Morgan Branham and Andrew Jackson Ferrell in April 1850.
1850 - Census house #78 James and Eliza Herdon Ferrell Morgan (Andrew Jackson Ferrell in household also) Letcher Co, KY.
1850 - Census house #78 Betsy Branham (4 month old Wm Jennings Branham in household) Letcher, KY

Handwritten notes by James Taylor Adams on file in Clinch Valley College, Wise, VA - state the following" Joseph Branham was "killed" when his brother "Turner struck him with a shot gun" died before 1850.
Grandsons of Wm Jennings Branham knew that their grandfather's surname should have been Ferrell, as their father, William Branham had told them both when they were in their teens. They also knew they were part Iroquois.

Betsy followed Andrew Jackson Ferrell to Scioto, Ohio, And he followed her and their son to Minnesota. They never marry but remained close to one another, as did their children.
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Birth	Apr 1850	Taylor Co, Kentucky, United States
Marriage	18 Feb 1872	Stearns, MN - Mary Ann "Annie" Baker
Death	Abt 1919
Census (family)	1885 MN State Census	Krain Twp, Stearns, Minnesota, United States - Mary Ann "Annie" Baker
Burial		Hawley Cemetery, Hawley, Clay, Minnesota, United States

Spouse	Mary Ann "Annie" Baker (1853 - 1930)
Child	Maude "Maudy May" Branham (1889 - 1975)
Child	Polly Branham (1872 - )
Child	Jane Branham (1874 - )
Child	Forest Albert Branham (1874 - 1956)
Child	Mary Elizabeth "Lizzie" Branham (1875 - 1962)
Child	George Henry Branham (1876 - 1966)
Child	Nancy Ann "Nan" Branham (1878 - 1957)
Child	Martha "Marthy" Branham (1879 - 1962)
Child	Joseph Harrison Branham (1880 - 1913)
Child	William Andrew Branham (1881 - 1970)
Child	Noah S Branham (1883 - 1974)
Child	Alameda "Meedy" Branham (1886 - 1955)
Child	Jesse Valentine Branham (1887 - 1957)
Child	Ada Branham (1888 - )
Child	Aggie Branham (1888 - )
Child	Effie B Branham (1894 - 1967)
Child	Girl Branham (1894 - )

Father	Joseph Branham (1810 - 1850)
Mother	Elizabeth "Betsy" Morgan (1816 - 1883)
Sibling	Susan Branham (1835 - )
Sibling	Isom Branham (1836 - )
Sibling	Eliza Branham (1841 - )
Sibling	Martha Branham (1842 - )
Sibling	Milly Branham (1845 - )

Notes