The following is possibly Joseph's son, but has not been proven (or disproven, for that matter).  The evidence is entirely circumstantial and not convincing — it's my own  family's legend that is probably untrue:
3.  Isaac DAVIS, b. 1760-65
What is true and what no doubt led to the birth of our family legend is that this Isaac DAVIS and his family lived from ca. 1797 to 1818 in the watershed of the West Fork of the Red River, near Fairview, Christian [now Todd] Co., KY, birthplace of Jefferson DAVIS in 1807/8.  The legend is reinforced by the fact that Isaac and his wife's kin had come to the West Fork region from Broad River, in South Carolina, the last certainly known location of Joseph DAVIS.

According to Barb (1971: 497):

There appears no means of knowing whether or not Joseph was ever married and had issue, but I regard the likelihood of it as very improbable.  It is certain that he had not married as late as 1762, at which time he signed a deed which will be cited later [Source 3, below], and which would have required the signature of his wife, had he had one, to make it legal.

Barb's statement that Joseph most likely died without issue is without foundation and a bit surprising, given how well documented and reasoned the rest of his paper is.  At present, there is very little known of Joseph DAVIS, certainly not enough to declare with any certainty that he died without issue.  All the 1762 indenture suggests (does not prove) is that Joseph had no wife at the time he signed it.  It is possible that he had been married before and was a widower with children in 1762 or that he may have married after 1762 and had children later — or both.  And it's also possible that Joseph did have wife at the time, but given the length and difficulty of the journey, she did not come with him to Philadelphia and that, rather than delay the proceedings, everyone simply tacitly agreed to go forward without observing the legal niceties, if he even admitted to them that he was married.  And the next paragraph describes in what other ways they weren't being terribly punctilious about observing the law…

That one should not place too much emphasis on a single document, especially this indenture, is futher confirmed by the fact that neither Evan DAVIS, Jr., nor his wife or son are mentioned in it.  This fact has been taken to mean that Evan DAVIS, Jr., had died before 1762, which I don't believe anyone disputes; however, his wife should have been a party to the indenture as his widow and heir, but she is not mentioned.  It may be that Evan's siblings were unaware of her and her son's existence (down in Georgia) or that attempts to locate them had failed or — one is reluctant to believe — that they were simply willing to defraud her and her son of their rightful inheritance.  In any case, the fact that they weren't mentioned in the indenture cannot be used as proof they didn't exist, especially as we know that they did exist.  Similarly, I cannot accept this document as proving that Joseph never married or had children (ditto his brother Benjamin). 

Joseph DAVIS signed the indenture in 1762 in Philadelphia as being "of Broad River, South Carolina."  There is a Joseph DAVIS in the Broad River region of NC/SC who deserves some investigation as to whether he is Evan's brother.  Below is a timeline (extracted from a larger timeline constructed for a different purpose) of  events surrounding one Joseph DAVIS in the Broad River regions of NC/SC .  I have included in the timeline here individuals in that region known to have moved to Christian/Todd Co., KY, in the late 1790s.  The CLARKs, KUYKENDALLs, WYATTs, FRENCHes, WHITESIDEs, and DAVISes settled in the "West Fork Region" of the Red River watershed in what is now mostly Todd, partly Christian, County, that is, in the region of Fairview, birthplace of Jefferson DAVIS.

Lastly, my family — like many a southern family with DAVIS ancestors — has a tradition of being cousins to Jefferson DAVIS.  Most of these traditions are untrue, many without the remotest foundation (e.g., see these bogus ancestries of Jefferson DAVIS).  And I should precede my comments with the disclaimer that I am, by nature, a skeptic, and I don't believe any family legend until it is proven true — I've just seen too many proven untrue when exposed to scrutiny.  However, our DAVISes were living in the West Fork Region of Christian/Todd Co., KY, near Fairview, from the late 1790s until 1818 — the same time period when Samuel DAVIS, father of Jefferson, lived in the region — so I don't think my family can be faulted for having accepted such a tradition for generations.  However, I do not want to believe it if it isn't true, so my starting position is that it is not.  The evidence must convince me otherwise and, as it stands, there is only one possible avenue open to us as a connection is through Joseph DAVIS of Broad River, South Carolina. 

(Please see Jefferson Davis Home Page for a general discussion of the possibilies for connection to the late CSA President.)

1.  Kirk Bentley Barb.  1971.  "Extract from Genealogy of Jefferson Davis."  Appendix III, pp. 488-508 in Papers of Jefferson Davis, Volume 1, 1808-1840.  Haskell M. Monroe, Jr., and James T. McIntosh, eds.  Louisiana State Univ. Press, Baton Rouge.  [Rev. ed. of 1991 not seen.]

2.  Will of Evan Davis, Sr., 1743, in which he names his wife and children. 

3.  Indenture, 1762, in which William Davis buys out his siblings' interest in real estate bequeathed to them by their parents.  This document tells us that, at the time, Joseph Davis, carpenter, was "of Broad River in the Colony of South Carolina" and that he came to Philadelphia to be present at the settlement. 

4.  Haskell M. Monroe., Jr. & James T. McIntosh, eds.  1971.  "Genealogy of the Davis Family."  Appendix IV, pp. 505-529 in Papers of Jefferson Davis, Volume 1, 1808-1840.  Louisiana State Univ. Press, Baton Rouge.  [Rev. ed. of 1991 not seen.]

5.  Ernesto Caldeira.  1983.  "Davis Family Genealogy."  Appendix II, pp. 402-416 in Papers of Jefferson Davis, Volume 4, 1849-1852.  Linda Lasswell Christ, Mary Seaton Dix, and Richard E. Beringer, eds.  Louisiana State Univ. Press, Baton Rouge.

6.  Paul R. Sarrett, Jr., compiler. [nd] Some "Early" South Carolina Marriage Records: 1641-1799 (online in the SCGenWeb Archives; file: sc-g1800.txt).