Building on the definition of a Paranormal Story (as opposed to Dark Fantasy) described in the answers here: What are most common tropes of a paranormal book and dark fantasy book?.
A paranormal story is about a phenomenon that cannot be explained in-world. It defies natural laws, probably logic and common sense, too. Borrowing a rule from the link, a story with an incidental paranormal element isn't a story about a paranormal element.
I don't want to be too narrow on defining what counts as paranormal. The genre is Horror so inclusive of traditional ghost stories, elements which are left intentionally ambiguous, and stories that evoke the supernatural even if it is rationally or psychologically explained.
The Paranormal Story can be a subplot or smaller section of a larger story. The question is about how to structure just the paranormal parts of the narrative, in practical terms, they way they might be plotted as story beats on a timeline.
What is the structure of a Paranormal Story?
I was only able to think of 2 paranormal story structures:
Evidence of the paranormal – the phenomenon is incrementally introduced, allowing characters to discover, debate, and rationally reject each in turn. Circumstantial evidence and unreliable testimony build, creating conflict and division among the characters – or self-doubt in a single character. The inevitable climax is a confrontation or direct encounter with the paranormal, which resolves the conflict – either the supernatural is confirmed as true, it is rationally explained through a plot twist, or ambiguity is preserved.
Descent and return – when the phenomenon is unambiguous, it's presented as a dark mirror or alternate reality to the normal world, with a threshold or barrier which can be circumvented, fails, or acts as a portal. The protagonist intentionally or accidentally descends into the paranormal world which becomes stranger and more threatening the deeper they go. The conflict is about navigating back to the normal world, or the consequences of bringing back a compromised object or entity which should not exist in the normal world.
I am able to think of many other structures for horror stories in general, and this feels broadly adaptable to co-exist with other horror themes, but when I thought critically about what keeps a paranormal story about the paranormal – as opposed to transitioning into a monster chase or some other type of horror story – these were the only ones I could think of.
Are there others?