I have a Fatigue system in one of my in-development games but (to grossly oversimplify) it's an Azure Dreams or Rune Factory kind of game that mixes a life sim with dungeon exploration and the point of Fatigue is to ensure that the player doesn't spend ridiculously long amounts of time (and make too much progress) in the dungeons without returning to town to relax, change up the pace, and get to know the world and characters better.
The way I implemented it is to have Fatigue build up with each battle, as well as with passing time; as you get tired (~75% fatigue), your stats and regen start to drop slightly, and as you start running on empty (beyond 100% fatigue) they drop a lot. At 150% fatigue you faint, which is a Game Over in the dungeons or costs you a lot of hours (since sleeping on the streets doesn't charge you up quickly) if you're in town. You can use drink items (sodas, potions, coffee, slushies) to relieve a fixed amount of Fatigue, but the accumulation of Fatigue scales up - for example, the first dozen hours you're up in a row might add 2% fatigue apiece, the next few hours would add 3% apiece, and then the amount would increase by 1% per hour, so that by 24 hours without rest, you're accumulating 15%+ fatigue per hour which makes it impractical to stay up for extremely long periods.
I thought about making Fatigue a per-character stat, but decided against it. Yes, it's realistic, but also very inconvenient for the player. Much smoother experience to let them just think about one number for the Party than managing it for everyone. For a more traditional dungeon-crawler with a large party, you might do Fatigue per-character as a way to encourage players to use their entire party, but for my game doing so doesn't make sense.
Anyhow, that's a fair bit of rambling I did about my own game, my point being that the system should have some kind of clear reason and positive gameplay function in your game (because otherwise it will just be an unnecessary annoyance), and that you should be careful about making Fatigue-relieving items (because unless you introduce other mechanics to prevent abuse, you might be negating the original purpose of having a Fatigue system in the first place).