Jag
wiktionary
The noun is from late Middle English jagge, the verb is from jaggen.
Circa 1597; originally "load of broom or furze", variant of British English dialectal chag(“tree branch; branch of broom or furze”), from Old English ċeacga(“broom, furze”), from Proto-Germanic *kagô (compare dialectal German Kag(“stump, cabbage, stalk”), Swedish dialect kage(“stumps”), Norwegian dialect kage(“low bush”), of unknown origin.
etymonline
jag (n.1)
"period of unrestrained activity," 1887, American English, perhaps via intermediate sense of "as much drink as a man can hold" (1670s), from earlier meaning "load of hay or wood" (1590s), of unknown origin. Used in U.S. colloquial speech from 1834 to mean "a quantity, a lot."
jag (n.2)
"slash or rend in a garment," c. 1400, of unknown origin.