Puckish American comic Billy Crystal strikes out in a new direction as the star of the limited series “Before,” premiering Friday on Apple TV+. Let us say at the outset that he is completely able to handle the assignment. The assignment itself is something of a mixed bag, but at no time will you think, “Billy Crystal isn’t up to this.” In fact, it could have used a little more of what he’s famous for.

With its chilly mood, supernatural business and central relationship, between a child psychologist (broken) and a young child (frightened), it should remind anyone who has ever seen “The Sixth Sense” of “The Sixth Sense.” Which, of course, was a very successful movie.

Crystal plays Eli, on the verge of retirement, who discovers a mysterious, silent 8-year-old boy with bloody fingers scratching what looks like a message into his front door. The boy runs away, later sneaking into Eli’s house through the dog door; Eli in turn follows the child, whose name is Noah (Jacobi Jupe) back to the apartment of his doting foster mother, Denise (Rosie Perez). When a colleague calls him back to consult on an especially difficult, violent case — we understand from this very request that Eli’s good at his job — it will, not surprisingly, turn out to be this very boy.

Rosie Perez plays Denise, who fosters Noah (Jacobi Jupe), a troubled boy who is nearly mute.

(Apple)

Noah barely talks — he screams quite a bit, including in 17th century Dutch — but draws lots of pictures, most of which are disturbing and obviously meaningful and all, or nearly all, feature the image of a farmhouse, the very image of a photo tacked up on Eli’s refrigerator. While the professionals scratch their heads, we can see that his acting out is only a reaction to whatever thing or condition or cosmological prank is torturing him.

It happens that Eli’s late wife, Lynn (Judith Light), who’ll appear in flashbacks, dreams and hallucinations — there’ll be a lot of those — and whose death Eli will not admit he’s not over, was a writer and illustrator of children’s books. One of her own drawings, a sort of Hansel and Gretel scenario, will also play a part in the action, which is ripe with echoes and reflections and uncanny parallels, along with dead people who might be ghosts or visions or psychological projections, or some combination thereof.

Eli feels a strong connection to Noah, sometimes feeling what he feels, but as a man of science, he frames it as “some extreme case of transference-counter transference.” His friend Jackson (Robert Townsend) suggests there might be a spiritual connection between the two, “some kind of continuity of existence,” and that ayahuasca might be the way to go. It gives Crystal one of his rare openings for a laugh line, “Say hi to your shaman, wish him a happy 1969 for me.”

Hackles unreasonably raised, Eli will continue for a while to beat that drum. “You believe in fairy tales created to keep people from facing the truth,” he says to a priest at the church where Noah, an abandoned baby, was found. “There is no magic being living in the sky looking out for us.” Of course, when someone says, “There’s no such thing as ‘beyond science,‘” in a movie or television show, science is almost always going to finish second (“The Big Bang Theory” was a more radical show than I may have previously realized), whether the supernatural forces are for good or evil. In either case, it’s always going to be the skeptic who has to change his way of thinking, because that’s the show-business America we live in.

Jacobi Jupe is impressive in a role that requires mute expressions of fear.

(Apple)

The mood is macabre throughout, with spooky sounds and music and a cloudy palette so that there are few bright, normal moments to measure the surreal frights against. There’s no sense that things are going to get spooky, because they’re pretty spooky from the beginning, and though they become spookier as the series goes along, they are almost never not spooky.

Crystal does fine in this environment; he doesn’t come off as a tourist or a dilettante. Jupe, 11, but looking every inch 8, is impressive in a role that requires mute expressions of fear, anger, affectlessness, distrust and panic. And there are nice supporting performances, from Hope Davis as a doctor even less ready than Eli to accept the uncanny, and Miriam Shor as an annoying real estate agent, weirdly anxious to sell Eli’s house out from under him, the only real comic part in the piece.

Created by Sarah Thorp, the series, which runs 10 episodes, wisely doles them out in portions of half an hour or less — but five or so hours is still a lot of time to maintain the tension in a psychological thriller, and “Before” doesn’t really manage it. It moves slowly until the accelerating endgame, urged forward by a ticking clock. There is also more than a bit of repetition — scenes played in different settings, with different energies, props and clues, but making more or less the same point, even as the series lopes bit by bit toward a conclusion.

But many revelations are telegraphed well in advance, and as things grow more obvious, they become less engaging. One hangs around, finally, to know whether the ending will be a light one, a dark one or a light one that flips to dark in the final seconds. I will not say which.