This is Little Sadie This is what the Traditional Ballad Index says:
Bad Lee Brown (Little Sadie) [Laws I8]

DESCRIPTION: The singer goes out one night to "make his rounds." He meets his (girlfriend/wife), Little Sadie, and shoots her. He flees, but is overtaken and sentenced to (a long prison term/life)
AUTHOR: unknown
EARLIEST DATE: 1922
KEYWORDS: murder prison
FOUND IN: US(Ap,So,SE)
REFERENCES (5 citations):
Laws I8, "Bad Lee Brown"
Randolph 155, "Bad Lee Brown" (2 texts, 1 tune)
MWheeler, pp. 109-111, "Late One Night" (1 text, 1 tune)
Lomax-ABFS, pp. 89-91, "Bad Man Ballad" (1 text, 1 tune)
DT 659, LILSADIE*
RECORDINGS:
Clarence Ashley, "Little Sadie" (Columbia 15522-D, 1930; on RoughWays1)
Wade Ward, "Little Sadie" [instrumental] (on Holcomb-Ward1)
ALTERNATE TITLES:
Bad Man's Blunder
File: LI08

So neither Johnny Cash nor Bob Dylan invented it. Though there are people out there on the web who claim it for those folks.