From The Folk Music Index:
(The index is by no means all-inclusive. If Jailhouse Blues is where the Rodgers song came from, there's GOT to be an earlier recording.)

Jailhouse Blues

Hopkins, Lightning (Sam). Blues in my Bottle, Prestige Bluesville OBC-506, LP (196?), cut# 7

Watson, Doc and Merle. Pickin' the Blues, Flying Fish FF-352, LP (1985), cut# 6 (Jail House Blues)

Wilkins, Robert. Original Rolling Stone, Herwin 215, LP (1980), cut#B.02

In the Jailhouse Now - Rodgers, Jimmie

Bookbinder, Roy; and Fats Kaplan. Git-Fiddle Shuffle, Blue Goose 2018, LP (1975), cut#B.02 (He's in the Jailhouse Now)

Cooney, Michael. Singer of Old Songs, Front Hall FHR-007C, Cas (1976), cut# 10 (I'm in the Jailhouse Now)

English, Logan. American Folk Ballads, Monitor MF 388, LP (196?), cut#B.03 (He's in the Jailhouse Now)

Jackson, John. Deep in the Bottom, Rounder 2032, LP (1983), cut# 9 (He's in the Jailhouse Now)

Reed, Bud. Way Out On The Mountain, Folkways FTS 31092, LP (1982), cut# 2

Rodgers, Jimmie. First Sessions, 1927-28, Rounder 1056, LP (1990), cut# 11

Rodgers, Jimmie. Short But Brilliant Life of Jimmie Rodgers, RCA (Victor) LPM-2634, LP (1963), cut# 4