I don't know if there is a connection or not. What part of Texas are you in?
My LITTLEFIELD LINEAGE
(1) Thomas R. Buckner
(2)G. R. Buckner and
Callie Mae Davis
(2) G. R. Buckner was the son of:
George Riley Buckner and
(3) Ada Lee Littlefield, daughter of
(4) James William Littlefield, b. 1844, Probably Spartanburg, SC, d. 1917, Park Springs, TX, and
Julia Ann Holt, b. 1848, Place ???, d, 1907, Park Springs, TX, (I have a copy of their marriage certificate dated 6 Feb., 1868, Gibson County, Tennessee) daughter of:
David Holt, b. 1802, Cumberland Co., NC, d. 26 Jan. 1865, and Nancy Elizabeth Shane
David Holt was probably the son of John or David Holt (no other information), who was probably the son of Frederick Holt (no other information).
Family tradition has it that the Littlefield lineage is connected to David Crockett although I have not been able to document this.
Additionally, the Littlefield family has always told its children that it had Cherokee lineage. I cannot confirm this although I would like to establish such a connection.