A full list of 50+ Chronomancy spells, plus related monsters, items, backgrounds, etc, can be found in the comments of my Chronomancer (Wizard) subclass here.
https://www.dndbeyond.com/subclasses/6582-chronomancer

Chronomancer, Version 2 - [https://www.dndbeyond.com/subclasses/522102-chronomancer]

Should require a saving throw when cast.

Dormammu, I've come to bargain.

:D

Hi HalfElfMonk,
The first save the creature makes is at the end of the round the spell was cast, before it repeats any actions for the first time.  Which is essentially the saving throw vs effect.  Saves on subsequent rounds (with cumulative bonus) could be seen as the save to break free.

hehehe

If it is in the creatures mind, wouldn't it make more sense as Illusion magic?

I think I get where you're coming from, but I don't think so.  Typically, things that alter state of mind, hypnosis, altering thoughts, etc, are Enchantment ; while things that alter sensory input, or produce actual false effects (photons and images, sounds, smells, etc) are Illusion.

In this case, the spell isn't tricking the target into thinking they should do the same thing over and over - it's actually resetting the physical state of their brain every round, to cause the creature to be stuck in a loop of decision and action.

The cumulative bonus corresponds to the increasingly desynchronized (and thus jarring) disparity between what the target remembers and expects about their immediate surroundings, vs what the surroundings have changed to each round  as time advances "without them".

You might have a valid argument for Transmutation instead, but I still believe Enchantment might be the better fit.

That said, if you want to create a spell that makes the target BELIEVE they are actually stuck in a time loop by looping their sensory input, and thus they think they need to keep taking the same action over and over Groundhog's Day style, I think that's a cool idea, and would fit the Illusion school.  That's a really valid reinterpretation of this spell if you want to play an illusionist.

Incredible explanation!! Cheers, great ruling

Thank you!