Green’s Dictionary of Slang

(US) used in mild oaths as a euph. for Jesus! excl.

1887		G. Davis Recoll. Sea-Wanderer 330: ‘Jimminetti, no,’ said Mr. Hamlin. ‘You wern’t so darned slow; hey, ’Squire?’.
1901		Monroe & Northup ‘College Words and Phrases’ in DN II:iii 142: jiminetty, interj. Used in surprise, anger, etc.
1909		Van Loan ‘A Job for the Pitcher’ Big League (2004) 69: Great Jimminetty! [...] Boy, look quick!