I would expect they are like the older Admiral Kuznetsov class and carrying the SU-
33 or Yak-141 (or newer YAK-43 design), possibly both.
They could also be reviving the older Kiev class "Heavy aircraft carrying cruiser".
It is important to know that previous Russian naval air doctrine was to use the CV in
a support role, not as the central attack force of the battle fleet. Therefore Rissian
designs have been much smaller than typical American CV's.
Edited: Added picture
Currently Russia's only deployed CV, The "Admiral Kuznetsov"