These two novels came out a year apart. They share certain very noticeable similarities:
The setting is nominally the real world, but children are occasionally born with paranormal potential; however, it's implied that they rarely attain the awareness and training needed to properly harness that potential. The plot centres on a covert conflict between two small groups who have attained control over their powers, but continue to spend time in public interacting with "normals". The antagonists, who are shown early on recruiting a new member in their late teens, have achieved eternal youth using an elixir that they must occasionally replenish by identifying children from the general population with latent powers, using their knowledge of those powers to tempt the children away from safety, and then extracting their life force. The principal point-of-view character has some powers and receives limited mentoring, but one of the main supporting characters is a self-taught child with exceptional power; the two have a family-like bond. The antagonists, despite their eternal youth, are still mortal, and are eventually defeated through mundane means. The climactic confrontation takes place in a location with paranormal properties that the point-of-view character recalls from their youth, and features both a labyrinth and the release of other entities which had been trapped inside the point-of-view character's head. One of the protagonists dies, but is shown to live on; the antagonists have no such afterlife, and are utterly destroyed.
The Bone Clocks, by David Mitchell, was acclaimed by Stephen King, who wrote Doctor Sleep. (Both are high-profile authors working in related genres; for what it's worth, an otherwise unrelated movie.stackexchange question notes that each author includes connecting elements between his stories.) This is all circumstantial and while it feels suggestive to me, I can also believe that it might be coincidence as Mitchell implies in the interview I linked to above. Is there any stronger evidence either way?
I don't think either King or Mitchell would be daft enough to intentionally plagiarize the other. I'm more curious to what extent the very specific common elements could have spread through broader sharing of ideas (in either or both directions) whether through direct conversations, or more likely via some of the common circles that authors move in: conventions, interviews, etc.
Sorry if this is too open-ended. My hope is that by asking specifically for strong evidence as opposed to conjecture, it will fall on the safe side of the line, but perhaps no such evidence exists, and regardless I recognize that these things can be a bit grey.