Puella Magi Madoka Magica certainly has Psychological Horror elements. its structured a lot like a mystery so beware clicking on this spoiler, it will take some reveals Away from the show. it's Fucking Amazing although At The Time was pretty experimental and the animation funding is iffy at times. the writing is impeccable though. if you enjoy the show you have to watch Rebellion, just because it's amazing to see what they do with an actual animation budget, and it also wraps up sooo many of the questions you're left with for a much more satisfying ending.

I think "Another" pulls off a Final Destination type story line much more efficiently than anything else i've seen attempt it, but it's still pretty mid at the end of the day, i have a soft spot for it though

i've never finished Paranoia Agent, but its directed by Satoshi Kon and is quite unsettling. because it's Kon it's a lot more respectful than the two above as well. would reccomend this one if you're looking for something Think-y and Critically Well Done. it is the only TV show Kon did before his death (although he has a lot of movies)

overall though, i'll say anime is not really well known for having a ton of super well done horror. both Paranoia Agent and PMMM aren't really trying to be dedicated horror shows, and most of the ones that Are are known for being gore-fests, exploitative about female characters, etc. Basically it's one of those genres that's sadly very "anime" so you tend to have to look for psychological horror or other genre-fusions.