born: February 1812
died: 
Oral tradition and notes from Ola Williams and Mattie Williams states that Minerva Fannin was the daughter of Col. J. W. Fannin who commanded at Goliad, Texas and died in the massacre there in 1832. However, Col. Fannin was born too late to be her father. It is more likely that he was her cousin.
Col. Fannin married Minerva Fort and had a daughter named Minerva J. Fannin, born in 1832. His uncle, Joseph Decker Fannin, married Betsey Low and had a daughter named Betsey Minerva Fannin,  whose data closely matches Minerva Fannin, wife of William W. Williams. This Betsey Minerva was born in 1812 and died in Talladega County, Alabama. However, she was married to Seaborn Johnson and bore several children to him in the 1830s.
One undocumented source also lists a Betsey Minerva Fannin as a daughter of William Y. Fannin, brother of Isham Saffold Fannin and Joseph Decker Fannin. If this source is correct, Minerva wife of William Williams may be Betsey Minerva, daughter of William Y. Fannin. Older family members stated that the mother of Baron DeKalb Williams was "Hester Minerva Fannin" -- it is possible that they were misremembering "Betsey Minerva" due to confusion with the name of Baron DeKalb Williams' daughter Hester Ann Minerva Williams (who was probably named Hester Ann for her maternal grandmother Hester Ann Perkins, and Minerva for her paternal grandmother Minerva Fannin).
Another possible father for our Minerva is Jeptha Fannin, son of James Fannin and Elizabeth Safford and brother of William Y. Fannin. Jephtha Fannin appears on the 1820 Morgan County, Georgia, Census (Cook's Dist.) with 1 male child under 10, 2 males 26-45, 2 females 10-16, 1 female 16-26, and 1 female 26-45. 1830 Morgan County, Georgia, Census, with 3 male and 4 female children under the age of 20. His recorded marriage to Cathrine Porter is in 1814 (after our Minerva's birth), however he might have been married previously. Jephtha was born 17 February 1785 in Greene County, Georgia. There is a William Williams recorded as living in Morgan County in 1824 in Tolbert's Dist. who might be the father of our William Wesley Williams. 

I find two other Fannins marrying in Newton County, Georgia, around the same time as our Minerva. Perhaps they were sisters:
Coney Fannin m Daniel Hopkins 20 December 1825
Polly Fannin m Robert Rawlings 7 December 1825

Newton County was created in 1821 from the parent counties: Henry, Jasper, and Morgan. 1820 Georgia Census lists Jeptha Fannin in Morgan County. 1810 Georgia Census lists "W. Fannin" in Franklin County.

William Fannin married Catherine Martin 18 January 1807 in Green Co., Georgia
Isham Fannin married Peggy Porter 1 September 1809 in Green Co., Georgia
Jeptha Fannin married Catherine Porter 10 May 1814 

Father: (possibly) William Y. Fannin
Mother: Catherine Martin

Spouse: William Wesley Williams
Married:  26 December 1830 in Newton County, Georgia

Children:
1.  Nancy Farr Williams
2.  William LaFayette Williams (m. Henrietta Adeline Floyd) PHOTOGRAPH
3.  Baron DeKalb Williams
4.  Sarah Caroline Williams
5.  Elizabeth Flora Williams
6.  Annis Minerva Williams (m. Coleman Pendleton Motley II)
7.  Rufus Pitt Williams (m. Martha Jane Roberson, Nancy Clark Atkins)
8.  Martha Jackson Williams
9.  John Hampton Williams
10. Thomas Cooper Williams (m. Ellen Robertson)