1905, "of an indefinite number," originally Morse code slang for "dash," influenced by association with numerals such as twenty, thirty, etc.
Online Etymology Dictionary, © 2010 Douglas Harper
Examples from the Web for 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.