Green’s Dictionary of Slang

to punish, to beat, to scold soundly; sometimes used with other verbs, such as administer; also with catch/get, to be punished.

1840		Boston Transcript 12 Feb. 1/1: If any of you ever come to Saco, I kalkilate you’ll get jesse [DA].
1846		Spirit of the Times (N.Y.) 4 July 223/3: One of the combatants ‘caught Jessie’ [DA].
1847		J.S. Robb Streaks of Squatter Life 33: Well, hoss, you’ve slashed the hide off ’er that feller, touched his raw, and rumpled his feathers — that’s the way to give him jessy.
1848		‘Ned Buntline’ Mysteries and Miseries of N.Y. V 63: By the piper what played afore Moses and the bull-rushes – that’s the feller I gived jessy to, last night!
1849		Jefferson Republican (Stroudsburg, PA) 19 July 2/5: [He] will make a pretty fair run, provoded he don’t ‘catch Jesse’.
1855		T. Haliburton Nature and Human Nature II 34: We always called it gray whackey in school, when a feller was catching particular Moses.
1858		T.G. Vielé Following The Drum 172: General Harney [...] hearing rumors of numerous filibuster and Indian troubles, had come down [...] to administer ‘jesse’ generally to all delinquents.
1860		Hotten Dict. of Modern Sl. etc. (2nd edn) 161: ‘To give a person jessie,’ to bat him soundly.
1862		Newbern Wkly Progress (NC) 26 July 1/4: Should these story-retailers succeed in getting him fairly roused, they will catch Jesse.
1867		Campaign with General Price in Schele De Vere (1872) 27: The old general turned round and said: Well, gentlemen, I think we have given them very particular Jessie on this field.
1872		Schele De Vere Americanisms 612: Jessie, to give, in the sense of giving a man a thrashing, is, perhaps, derived from the English slang phrase, unknown here, to give a man gas, through the (slang) adjective gassy. In the United States the popular phrase is made stronger by giving particular Jessie, or even d— particular Jessie, according to the greater or lesser violence of the speaker’s feelings.
1886		‘Ned Buntline’ Buffalo Bill 17: ‘Look out for yourselves, girls — the boys are giving ’em Jessie, and it's about time my hand was in’.
1888		Journal of Amer. Folklore I 78: When two American boys are fighting together and a crowd is watching the mill, a spectator will often encourage one of the contestants by crying, ‘Give him jessy!’.
1889		Waco Eve. News (TX) 25 Mar. 4/3: An attachment was issued for the witness [...] who will catch Jesse if not on hand to-morrow.
1890		Sporting Times 11 Jan. 5: Then he got the liveliest kind of ‘Jessie’.
1898		(con. 1875) F.T. Bullen Cruise of the ‘Cachalot’ 22: The harpooner got a good blow in, which gave the biggest of the three ‘Jesse,’ as he said, though why ‘Jesse’ was a stumper.
1906		Sun (NY) 13 Mar. 6/3: If the service is inadequate, the conductor is pretty likely to catch Jesse.
1946		AS Apr. 153/1: Thornton’s last citation for give him Jesse is from 1865 [...]. In February, 1946, I heard the expression used in a game of bridge by a player from Sidney, Nebraska [DA].