Depends who you ask, but it's absolutely not Mora. He scries fate, sees what is and could have been, and records it. He has no longer influence over fate itself.
Obviously they're setting up Ithelia, but she's been MIA for possibly centuries with no obvious loss of fate.
I think fate is just the choices you make (or don't) and the consequences, and nothing is pre-written. Some entities like to toss it around, but none of them got the ball rolling themselves.

The Creators of Fate to me would be all within the Aurbis that are able to make decisions that would or could change the direction of the thread or the path they are on unto another. Mephala I think contributes to changing directions of mortal fateline's if this is to be believed of her.

Mephala interferes in the affairs of mortals for her own amusement,[20][21] and does nothing without purpose.[4] Mephala thinks of the affairs of mortals as a weave;[16] pull but one thread and the whole thing unravels.[22] To her, the "web" of the Aurbis is an interconnected system of action and consequence, and she spins new threads to influence outcomes. In an essay analyzing the Daedric Prince, Divayth Fyr posits that Mephala likely doesn't see mortals as mere playthings, unlike some of her fellow Princes.[4]

https://en.uesp.net/wiki/Lore:Mephala

and maybe Hermaeus Mora asked a favor of Mephala - to cast a thread that might attract ones to his realm.:-
.....

Thoughts of Leramil the Wise on what Fate could be in this book: Master of the Tides of Fate

https://en.uesp.net/wiki/Online:Master_of_the_Tides_of_Fate

Soarora wrote: »

Ithelia. If we ignore her then I think fate is all possible outcomes into the future (the threads of fate), determined by gods upon those they control (ex. being Dragonborn), and maybe even the machinations of the Godhead.

Nah, I don't think so.

I don't actually think there is an answer to this, which means we are free to make up whatever we want.

So, my theory is that it isn't a "who" but a "what". I am going to suggest that it was a side effect of creating Akatosh. Time implies a before and an after and a connection between them. The connection is fate. I also hold that the connection is bidirectional, meaning that time and fate move from "before" to "after" in one of two directions.