Fudge
early 17th century: probably an alteration of obsolete fadge ‘to fit’. Early usage was as a verb in the sense ‘turn out as expected’, also ‘merge together’: this probably gave rise to its use in confectionery. In the late 17th century the verb came to mean ‘fit together in a clumsy or underhand manner’, which included facts or figures being cobbled together in a superficially convincing way: this led to the exclamation ‘fudge!’ and to noun fudge (sense 3 of the noun).
wiktionary
Probably a variant of fadge(“to fit”), the confectionery sense having evolved from the meaning of “merging together” or “turning out as expected”.
etymonline
fudge (v.)
"put together clumsily or dishonestly," by 1771 (perhaps from 17c.); perhaps an alteration of fadge "make suit, fit" (1570s), a verb of unknown origin. The verb fudge later had an especial association with sailors and log books. The traditional story of the origin of the interjection fudge "lies! nonsense!" (1766; see fudge (n.2)) traces it 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 without the necessary materials." The surname is from Fuche, a pet form of the masc. proper name Fulcher, from Germanic and meaning literally "people-army."
fudge (n.1)
type of confection, 1895, American English, apparently a word first used among students at women's colleges; perhaps a special use from fudge (v.) or its noun derivative, via the notion of "insubstantial" or of something "faked-up" on the spot. The verb was used in school slang, and compare fudge (n.) "a made-up story" (1797).
'He lies,' answered Lord Etherington, 'so far as he pretends I know of such papers. I consider the whole story as froth — foam, fudge, or whatever is most unsubstantial. ...' [Scott, "St. Ronan's Well," 1823]
fudge (n.2)
"nonsense, rubbish," (1791), earlier and more usually as a contemptuous interjection, "lies! nonsense!" Probably a natural extension from fudge (v.) "put together clumsily or dishonestly," q.v. But Farmer suggests provincial French fuche, feuche, "an exclamation of contempt from Low German futsch = begone."