Green’s Dictionary of Slang

(US) a countryman, a rustic; also attrib.

1947		E. Condon We Called It Music 83: This corncobber probably has heard Louis on a record and hasn’t any better sense than to think he can march in wearing that cap .
1970		Gaddis & Long Panzram (2002) 20: The significance of this was lost upon the overworked, morally indignant staff, which consisted mainly of local native ‘corncobbers,’ who gravitate to such work.
1997		Amer. Politics Journal 5 Nov. 🌐 Next thing you know, Virginians, who during the 80’s finally crawled out of there [sic] corncobber reputation, will secede, annexing themselves to the Vatican.
2001		Word for Word 🌐 It might look as though corny were one more piece of city slicker mockery of things rural, as in corncobber, a rustic and corncracker, a poor white Kentuckian. But the slang term corn is much older, and almost certainly influenced the jazz meaning.