I actually show an earliest date of 1898. Not sure where I got that -- probably from Doerflinger, since that's the book that caused me to enter the song, and I indexed it before I started explaining where dates came from. Bone dated it to 1900.

I'm pretty sure I first heard it sung by the Irish Rovers, on some record belonging to my parents.

The current Ballad Index entry looks like this:

Paddy, Get Back
DESCRIPTION: Shanty, with long chorus, "Paddy, get back, Take in the slack, Heave away your capstan," etc. The song details how the poor boy has to go to sea to earn money, then suffers at the hands of weather, mate, and a long voyage
AUTHOR: unknown
EARLIEST DATE: 1898
KEYWORDS: shanty poverty sailor abuse
FOUND IN: US(MA) Canada(Mar) Britain(England(Lond)) Ireland
REFERENCES (10 citations):
Doerflinger-SongsOfTheSailorAndLumberman, pp. 54-55, "Paddy, Get Back" (1 text, 1 tune)
Colcord-SongsOfAmericanSailormen, pp. 121-122, "Paddy Get Back" (1 text, 1 tune)
Hugill-ShantiesFromTheSevenSeas, pp. 321-327, "Paddy Lay Back" (3 texts, 3 tunes with variants) [AbEd, pp. 241-244]
Hugill-SongsOfTheSea, p. 32, "Pady Lay Back" (1 text, 1 tune)
Shay-AmericanSeaSongsAndChanteys, pp. 68-70, "Paddy Get Back" (1 text, 1 tune)
Kinsey-SongsOfTheSea, pp. 73-74, "Valparaiso Round the Horn" (1 text, 1 tune)
Kane-SongsAndSayingsOfAnUlsterChildhood, p. 124, "'Bout ship's stations, boys, be handy" (1 fragment)
Smith/Hatt/Fowke-SeaSongsBalladFromNineteenthCenturyNovaScotia, pp. 42-43, "Lay Out, Tack Sheets and Haul" (1 text)
Palmer-OxfordBookOfSeaSongs 141, "On Board the Leicester Castle" (1 text, 1 tune)
DT, PADLAYBK
Roud #653
RECORDINGS:
George Ling, "On Board the Leicester Castle" (on Voice02)
Richard Maitland, "Paddy, Get Back" (AFS, 1939; on LC26)
CROSS-REFERENCES:
cf. "The Liverpool Song" (form, lyrics)
ALTERNATE TITLES:
Mainsail Haul
The Liverpool Song
Valparaiso Round the Horn
File: Doe054