Green’s Dictionary of Slang

Jackson n.1

used in mild oaths as a euph. for by Jesus!

[US](con. c.1840) ‘Mark Twain’ Huckleberry Finn 106: By Jackson, I’d like to, and, blame it, I don’t know but I will.
[US]‘Mark Twain’ Pudd’nhead Wilson 106: By Jackson, he’s got you, Pudd’nhead!