Ok, let's go with a round of urban fantasy fics for @Lirica. Also ghost stories, because I think you may appreciate those as well. Maybe you had already read them, I don't know.
As I already mentioned, @GavotteAndGigue has written horror stories. The Dreamscape series is an enjoyable work, but not for everyone. It depicts heavy violence and the JayDick M/M ship, and it is a heavy plot point especially in the first story. It also depicts a disturbing other relationship. It's both supernatural and cosmic horror based on the Vertigo set of DC mythos (The Sandman, a bit of Hellblazer too), but even more Lovecraft-like. It's very pulpy, dark and gritty. Has constant allusions to noncon. Last part has Constantine on it. And a goat.
This writer has another work that I mentioned too, and that has finished just yesterday. It's supernatural and psychological horror, much like what you could find in a Silent Hill videogame. Phantasmagoria is better than the series I mentioned, not only because it's better written, but because it really crept the hell out of me half the time. It also depicts JayDick, but, eh, it's just barely there. Sick and hurt Jason gets stuck in a haunted building. A lot of confusing stuff happens. There are ghosts, demons and fire. They could have dubbed this work Red Hood: Silent Hill the Room. Mature content, because brutal violence basically.
Next work may not be a masterpiece, but heck if it didn't give me a lot of "feels" and put my heart in warmth. Tittle is: Call Me Dawnslight, by @InaudibleTacit. Technically, it doesn't play with different rules than the ones in the main DCU, but it plays them in a way that makes for an actual urban fantasy story. It's Bruce bonding and struggling with Jason, with dead Robin Jason. It's drama, and also healing, and a bit of mystery along the way. Really loved it.
One of the Batfics by @InsaneTrollLogic is a Ghost Story. Psychological horror with some supernatural elements. Very creepy, more because of the psychological stuff than of the supernatural.
Cycle of Life, by @chibi_nightowl isn't, strictly speaking, neither a ghost story nor urban fantasy; but I suspect you will like it if you don't mind the JayTim shipping. It's more like magic realism, to be honest: you could call it a "metafiction" work. And it's soft drama and almost a soliloquy by Jason.
I guess I can put The Many Deaths of Jason Todd by @Zoeleo in the "urban fantasy" category, but it's more like a mystery story with strong supernatural elements (I don't know if you can see the difference I'm trying to make). Mature content (violence, language and sexual content), M/M relationship. It's the first part of an unfinished series. The continuation is still ongoing, with a very slow pace; and so far it's mostly familial melodrama and fluff and shameless JayTim shipping that I think still needs a full plot to follow. I liked the first part a lot more.
@chibi_nightowl and @GoAwayOlivia are writing an urban fantasy series that I honestly don't know where it will go: Moon, Snow, and Ice. As you can guess, heavy JayTim shipping (there is also a past JayRoy implied, if I recall correctly). It's not main DCU Tim, at least: just a character that sounds like usual-chibi_nighthowl!Tim and shares his name (it's a fae). The rest of the characters though, are main DCU characters in their main DCU roles (or at least I think they are). Also, well, mature target for sexual content. The first part (which was a stand alone story at the time) was nice, and I honestly liked it enough for wishing for a continuation. I got lucky and now two writers I like have joined efforts. I trust them to finish this work, however long it will take: that's why I'm linking it despite how little they had released yet.
Eternal Soliloquy by @renecdote. Jason doesn't get brought back to life and is a ghost at his grave. Drama, general audience.
Jason, Meet John Constantine by @mizmahlia. Jason sees ghosts/other non-living creatures after coming back to life.
What was Left Behind by @Team_Alpha_Wolf_Squadron. While the pov is Damian in the first chapter, it's about him meeting young ghost!Jason. Teen audience. This work also has a small mystery story going on. And for those who have no qualms about violence and heavy sexual content of very dubious nature (if not straight noncon), this writer has a series that is both horror and urban fantasy. It's not as good as this short story, but in any case, the title of the series is He loves me.
Hell Connection, by @Ladelle. Jay/Tim ship, and it's targeted Teen, but as far as I recall, it's more like Mature targeted, really. It's not great, but if you like stories with demons and possessions and magic rituals and curses, this fic is quite enjoyable. Lots of melodrama and angst, but that's inherent to any grimdark story about demons.
Six Senses (And None of Them Common), by @Hinn_Raven. General audiences, no ships. This is a one shot, and a bit short; but it's a fun story with ghosts and I think you may like it.
Worth Living For, by @Myoneloveismusic. Teen audience, JayTim ship. This is also a one-shot, but a lot longer. Jason is brought back to live as some sort of guardian entity who is assigned to be the protector of a non-caped Tim from some dangerous monsters. I'll be honest: it's a bit bittersweet, but I enjoyed it. It's a fine story.
Tales from the House of Mau, by @clarityhiding. This is an urban fantasy, no capes series in which Jason inherits a comics and hobbies store (and an apartment) and ends being involved with the magic folk. None of the characters are with their original IDs and aliases; but those things sort of play into the story. It's male on male ship (JayTim. Female on female too, because IvyHarley), and even if it's tagged as teen, it's more like mature readers aimed, to be honest (by the commentary on sex themes). What can I say: it's fun, pretty chill and fluff in mood, and there are dragons and stuff. And tabletop roleplaying. Think "Fantastic Beasts" meets "Maison Ikkoku".
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There are way more stories with either ghosts or magic and supernatural elements in an urban setting in AO3. But either I haven't read them, or I disliked them, or the levels of shipping and sexual content are off charts, or the almost only trait the characters share with their DC counterparts is their name (making the whole fic almost not a fic, really). Or a combination of some of these reasons. I suspect there are even more in FFN, but it's a site I don't visit often and I usually struggle with the search engine there.