For what it's worth, the "jelly roll" referred to here is sexual slang of the early-to-mid 20th century. It refers to the female genitalia and is extended, via synecdoche, to mean a female sexual partner in general, and the song title suggests that the singer is not going to give anyone else access to his woman.
jelly-roll
1. the female genitalia
2. a sexual lover
Slang and Euphemism, Richard A. Spears, 1981
Now you know where early 20th-century jazz and ragtime musician Jelly Roll Morton got his name.
The "Ain't gonna [verb] nobody" or "ain't gonna [verb] no" is a hallmark of rural American and African-American speech dating to the 19th century and picked up wholesale especially in blues. White America began to borrow the construction with the advent of rock 'n' roll, which borrowed much from the black blues singers of the 1930s onward. Cf. the 1964 Rolling Stones hit "I Can't Get No Satisfaction."