I went back through some of my research and discovered that you are correct. Jesse Daniel Mings is not a son of Joseph Sr. Mings/Minzes. It is possible, I think very possible, that he is the son of one of Joseph's two brothers, James or Alexander. The problem is finding the evidence.
It is just one more of the mysteries of our family. Such as why did some take the surname "Mings" while others took the surname "Minzes" instead of keeping their father's surname "Menzies". There are records that show Joseph Sr. using the name "Mings" and yet I have seen records at the National Archives in Washington D. C. that have him going by "Minzes". Joseph Sr.'s second son from his first marriage, Joseph Jr., went buy the surname "Minzes" and it is through him that I am descended.
Joseph Jr. had a son named Ewing Shelby Minzes who was married twice and had traveled from Tennesee to Missouri just before the Civil War. In the 1880's at least two of his sons from the second marriage left Missouri and moved to Texas and dropped the "s" from their name. One of these brothers, Andrew Jackson Minze, was my Great-great Grandfather.
An interesting note: Andrew Jackson Minze was a Methodist Traveling Minister sometimes call Circuit Preachers. I think I recall reading something about some of Jesse Daniel Mings' descendants being Methodist Ministers and living in Texas.