A twist of fate
The earliest usage example of “twist of fate” I could find so far is from the mid 19th century:
“Pierre; Or, The Ambiguities” by Herman Melville - 1852 -
And now we behold this hapless youth all eager to involve himself in such an inextricable twist of Fate, that the three dextrous maids themselves could hardly disentangle him, if once he tie the complicating knots about him and Isabel. Ah, thou ...
You are asking about two different senses of twist. The first refers to some concrete physical item that has been twisted:
twist n
1. Something twisted or formed by twisting, especially:
a. A length of yarn, cord, or thread, especially a strong silk thread used mainly to bind the edges of buttonholes.
b. Tobacco leaves processed into the form of a rope or roll.
c. A loaf of bread or other bakery product made from pieces of dough twisted together.
d. A sliver of citrus peel twisted over or dropped into a beverage for flavoring.
And the second refers to a more abstract convolution, like an unexpected turn in a story or process:
- An unexpected change in a process or a departure from a pattern, often producing a distortion or perversion: a twist of fate; a story with a quirky twist.
The Free Dictionary Online
The noun form is attested from the mid-14th century, according to Etymonline:
mid-14c., "flat part of a hinge" (now obsolete), probably from Old English -twist "divided object; fork; rope" (as in mæsttwist "mast rope, stay;" candeltwist "wick"), from Proto-Germanic *twis-, from PIE root *dwo- "two." Original senses suggest "dividing in two" (source also of cognate Old Norse tvistra "to divide, separate," Gothic twis- "in two, asunder," Dutch twist, German zwist "quarrel, discord," though these senses have no equivalent in English), but later ones are of "combining two into one," hence the original sense of the word may be "rope made of two strands."