1905, "of an indefinite number," originally Morse code slang for "dash," influenced by association with numerals such as twenty, thirty, etc.
Examples from the Web for umpty
Historical Examples of umpty
And without the aid of a guide we located this Umpty Umpt street.Torchy As A Pa
But writing reminiscences of Umpty Squadron's early days is a melancholy business.
Over there a formation of A flight, Umpty Squadron, will perhaps be droning back from a hundred-mile reconnaissance.