The Shadow Behind the Stars by Rebecca Hahn
From Goodreads: A girl’s dark destiny could cause the unraveling of the world in this spellbinding novel from the author of A Creature of Moonlight, which Kirkus Reviews called “cumulatively stunning” in a starred review.
Heed this warning, mortal: stay far away from the three sister Fates. For if they come to love you, they might bring about the end of the world…
Chloe is the youngest. Hers are the fingers that choose the wool, that shape the thread, that begin it. The sun smiles upon her. Men love her without knowing who she is. She has lived forever and will live forever more. She and her sisters have been on their isolated Greek island for centuries, longer than any mortal can remember. They spin, measure, and slice the countless golden threads of human life. They are the three Fates, and they have stayed separate for good reason: it is dangerous for them to become involved with the humans whose lives they shape.
So when a beautiful girl named Aglaia shows up on their doorstep, Chloe tries to make sure her sisters don’t become attached. But in seeking to protect them, Chloe discovers the dark power of Aglaia’s destiny. As her path unwinds, the three Fates find themselves pulled inextricably along—toward mortal pain, and mortal love, and a fate that could unravel the world.