Two Suggestions drawing inspiration from Re: Zero - Starting Life in Another World and Steins Gate (both great stories involving very similar premises)
Re: Zero - Starting Life in Another World
Re: Zero - Starting Life in Another World is a Light Novel/Anime you could take inspiration from. The protagonist has a similar power with extremely large drawbacks. Quick Summary:
1. Protagonist (involuntarily) resets whenever he dies.
2. Dying is extremely unpleasant.
3. Protagonist can't control the save point at all.
4. Protagonist physically can't tell anyone about this power.
Restriction (1) is the most unique feature of this story. You could replace it with any other trigger you like, as long as it is involuntary, and is tied to an action that is unpleasant for the protagonist.
Restriction (2) is taken very seriously by the story: no matter how badly things go for the protagonist (short of death obviously), he has chosen to voluntarily die in order to reset only once, in order to undo the death of a close friend--no other method of revival exists in this universe, at least so far. Nothing else was sufficient motivation to voluntarily die, despite several very negative experiences such as his love interest and self-professed reason for existing breaking things off with him and other events with similar emotional impact. He would rather regain trust and try to win her back over over the following days/weeks than reset to wipe out the events of the last day. You need to take the psychological cost similarly seriously or readers will stop taking this cost seriously as well.
Restriction (3) is something you can decide to adopt or not based on whether it fits your story.
Restriction (4) --oddly enough-- actually increases the trust required between him and his companions for him to effectively leverage his ability. They have no idea he has foreknowledge, and he can't present any evidence to convince them. The plot sometimes dictates that he has to resolve multiple problems at the same time or near the same time in different places... He has to trust his companions to help him, because he physically can't resolve it all on his own, without being able to be open and honest about why. Saying "Do XYZ, Just trust me" only works if you are super close and have a great relationship with someone.
Steins Gate
Steins Gate is a visual novel/anime where the protagonist is a scientist with the ability to send information back in time (including directly to his old self's brain, effectively time jumping backwards). It's much more sciency and less magical, which may or may not be what you want. 425
There are a couple of interesting concepts that restrict his ability to exploit this to obtain whatever his heart desires:
1. Different timelines are woven together (think like you're following a single fiber in a rope. Even if you switch fibers, you're going to stay parrallel to the original fiber no matter how long you follow the new fiber) in a way which means "nearby" timelines all lead to similar outcomes, even if (superficially) there are large differences between them. A kind of anti-butterfly effect if you will, where nothing you do actually matters. Protagonist abuses this to make things better and better for him and his friends without radically affecting the world. Great!
2. It is possible to achieve radically different outcomes in only certain circumstances. To continue the rope analogy, imagine that you're following a rope fiber, and can only jump to other rope fibers that are in physical contact with that rope fiber. Usually that's another rope fiber within the same rope, but in the case where two ropes are laying across each other, you can actually make huge changes by jumping to a fiber in another rope. The drawback is that not every fiber in your current rope touches every fiber in the new rope. You may be forced to make lots of small tweaks you don't like in order to set yourself up to make the big jump you want to make. (This is actually the main problem facing the <PERSON> protagonist, he has to undo all the positive things he's done for himself and his friends in order to get back to a place where he can achieve an important outcome).
3. The limitation on how far back he can send information is based on biochemistry: Humans change over time. Our brain is continuously changing (not just by storing new memories and such, but also in response to long term trends in emotions: a depressed person's brain looks very different from a health brain). In order to do anything productive with a "jump back", you need your current memories. Writing your current memories onto your brain from 15 seconds ago is fine; they're so close physically (biologically and chemically) that they're effectively 100% compatible. 5 days ago is starting to get iffy, and 2 weeks ago is right out (the physical structure is too different). 209