These monsters are created by the Barians for the sole purpose of subduing the "Number" monsters. Xyz Materialsattached to "CXyz" monsters take the form of red diamond shaped crystals as opposed to glowing orbs, and are referred as "Chaos Overlay Units" in the anime.[1]
Like monsters that can utilize Chaos Xyz Evolution, these monsters require an additional Xyz Material but with 1 higher Level in a regular Xyz Summon, since they themselves are 1 Rank higher than their respective original counterparts.
So far, all of the "CXyz" monsters, except "Saimon, the Disciplinary High Priest", can inflict effect damage. Visually, they are all tied together by the presence of glowing red energy on their bodies, energy from the Barian World.
Trivia
This archetype is quite similar to "Meklord Emperor" monsters. Just as the "Meklord Emperors" are made to stop Synchro Monsters, "CXyz" were created to solely restrain "Number" monsters by being able to destroy them by battle despite their unique effect in the anime. They both can absorb specific targets to leave their opponents defenseless: "CXyz" can absorb Xyz Materials from the opponent's "Number", which are all Xyz Monsters, and "Meklord Emperors" can absorb the Synchro Monsters themselves.