The question I am asking is in regards to mutant rights ownership. Marvel Studios has already used a few comic book mutants in the MCU, such as Quicksilver, Scarlet Witch, and Quake. What other mutant comic book characters does Marvel Studios own, or at least can use?
As far as we know, none.
Scarlet Witch and Quicksilver are special cases: they are mutants, and always been associated with the X-Men, but they were also key figures in the Avengers since its founding. Marvel negotiated a shared licensing deal with Fox for those two: Marvel can use them in the MCU but cannot call them mutants.
Quake, in the comics, was never really associated with the X-Men. She was always a SHIELD / Avengers character. Though she was initially thought to be a mutant, it was revealed pretty early on that her powers likely came from her father's experiments, and not the X-gene that "X-Men mutants" have. (On a side note: Marvel has since retconned Daisy: she's now an Inhuman in Earth-616 as well, mirroring her back story in the MCU.)
It is, however, interesting to note that Quake was introduced into the comics in 2004 -- well after Marvel's deal with Fox. It's not conclusive (we have exactly one example so far), but it's possible that Marvel could bring in any newly-created mutant character from Earth-616. We don't know the specifics of the Fox deal, but it would not be unusual for it to contain an appendix literally listing the characters that cover it, and anyone not on that list is by default a Marvel property. (Again, this is all speculation.) What we do know, however, is that even if they did bring in such a character, they can't call them a mutant -- that term appears exclusive to Fox.
There have been several questions on this site about the character licenses, though they may be slightly out of date by now, including this one, and this one, as well as this one from our sister site.