Jeptha, Japhther, and Jafther are almost certainly misspellings of scriptural name, "Jephthah" (Judg. 11:1).

Brother:  Samuel GORDON (1761-1840), father-in-law of her son, Jephtha
Probable Kin:  John GORDON, b. bef. 1774

Given the age difference between Jephtha and Nancy, it's very probable he had an earlier wife.
Secondary sources are all over the map with regard to Nancy's birthyear and the year she married; so, obviously, everyone is guessing.  But given that she bore children between the years 1783 and 1808 and that the typical span of fecundity for a woman is about 23 years, her birthyear cannot have been much earlier or later than 1765.

— born in Garrad Co., KY:
  7.  Thomas Kennedy HOLLINGSWORTH, b. 29 Apr 1798; d. 26 Oct 1857
  8.  Enoch HOLLINGSWORTH, b. 1802
  9.  Samuel HOLLINGSWORTH, b. 1806
10.  Ruth HOLLINGSWORTH, b. 1808

"Asenith" is almost certainly a misspelling of the scriptural name, "Asenanth" (Gen. 41:45).
It's possible that one or more of the unnamed children born before 1790 were those of a prior marriage by Jephtha.

1.  Marriage Record:

2.  1790 Census Index/Images (online at Ancestry.com, Image #5 of 24; extracted by Diana Gale Matthiesen):

1790

SC

Greenville Dist.

Roll M637_11

p. 89

Ln. 6

Jafther Hollingsworth

1-2-4-0-4

These data indicate:

Gender and Type	Age Class	Therefore Born	Individuals Inferred
1 free white male	16 or over	in or bef. 1774	= Jeptha (b. 1745)
2 free white males	15 or under	1774-1790	= John Gordon (b. 1783) = Son A
4 free white females	all ages	in or bef. 1790	= Nancy Anne (b. 1768) = Asenith Ann (b. 1784) = Daughter A = Daughter B
4 slaves	all ages	in or bef. 1790	=

Given how our subject's given name was phonetically spelled here (i.e., with an "f"), I think we can be confident his name was intended to be the scriptural one, Jephthah.  It's possible that the unnamed children here are not Nancy's, but Jephtha's from a prior marriage.  Listed one line above John GORDON (1-2-2-0-0).

3.  1800 Census Index/Images (online at Ancestry.com):  not found, but the 1800 KY census was lost, and we know Jephtha was in KY by 1795 (see tax records, below).

4.  1810 Census Index/Images (online at Ancestry.com):  not found, and the 1810 KY census was not lost, so the best explanation is that our elderly subject is living with kin (i.e., not as head-of-household).

5.  Anon.  1991.  The 1795 Census of Kentucky [as constructed from tax lists].  T.L.C. Genealogy, Miami Beach, FL (said to include every extant tax list from every county existing in the state of Kentucky in 1795):

Pg	Name	County
84	Hollensworth, Japhtha	Madison
	Hollinsworth, John	Fayette
	Hollinsworth, Robert	Jefferson

This record further confirms that the pronunciation of our subject's given name included the "f" sound and was almost certainly based on the scriptural name, Jephthah. These are all the HOLLINGSWORTHs/etc. listed in the book.

6.  Anon.  1990.  Logan County, Kentucky, Taxpayers, 1792-1799.  T.L.C. Genealogy, Miami Beach, FL:  not found.

7.  LDS.  Family Search: Internet Genealogy Service:  IGI - International Genealogical Index (online at FamilySearch.org).

8.  LDS.  Family Search: Internet Genealogy Service: Pedigree Resource File (index to CDs, online at FamilySearch.org).

9.  WorldConnect / Ancestry World Trees (online at RootsWeb.com/Ancestry.com).