To quote Rick Riordan's website (located under Movies -> "There was a Percy Jackson live musical! What about a Percy Jackson TV show?"):
The rights for television/film to anything involving Percy’s world, including sequels like Heroes of Olympus and Trials of Apollo, are owned solely and forever by Fox. As far as I am aware, which is not very far, they have no plans to do anything further with those rights.
So - yeah, Fox owns the rights to Percy Jackson sequels. Now, this could be out of date, as the site also mentions only The Lightning Thief film being in existence (there's also The Sea of Monsters, curse them both). And as we'll see in a moment, it is kinda out of date.
The other ambiguity here is whether the Kane chronicles and Magnus Chase books count as sequels to the Percy Jackson books. I'd argue they are included as they are in the same world (the "other gods" reference in Kane Chronicles #1, the cross-over stories like Son of Sobek, and Annabeth Chase being the cousin of Magnus Chase), but I can't be sure there.
Now. There's another complexity. (Eesh.) The rights are being transferred over to Disney because Disney is
taking over the world buying a bunch of Fox, so (again quoting Riordan's blog):
Now it appears that many assets from the Fox movie studio will be bought by Disney, assuming regulators let the deal go through. I imagine that includes Percy, which means Percy Jackson, in a way, is “coming home” to Disney.
Wikipedia seems to agree that the deal includes Percy.
So...since Disney/Fox haven't technically fully carried through yet, it's all Fox right now. By mid 2019, though, it should be all Disney.