"put together clumsily or dishonestly," 1610s, perhaps an alteration of fadge "make suit, fit" (1570s), of unknown origin. As an interjection meaning "lies, nonsense" from 1766; the noun meaning "nonsense" is 1791. It could be a natural extension from the verb. But Farmer suggests provincial French fuche, feuche, "an exclamation of contempt from Low German futsch = begone."
The traditional English story traces fudge in this sense to a sailor's retort to anything considered lies or nonsense, from Captain Fudge, "who always brought home his owners a good cargo of lies" [Isaac Disraeli, 1791, citing a pamphlet from 1700]. It seems there really was a late 17c. Captain Fudge, called "Lying Fudge," and perhaps his name reinforced this form of fadge in the sense of "contrive ...