What happens if a Beholder places its Antimagic Cone over someone it has hit with its eye rays? Obviously the damage-dealing ones are instantaneous, but what about the charm ray, petrification ray, paralyze ray, sleep ray...etc.?
The effects of all rays with ongoing effects are suppressed.
From Antimagic Field (Which is the effect caused by Antimagic Cone):
Spells and other magical effects, except those created by an artifact or a deity, are suppressed...
From the beholder:
The beholder shoots three of the following magical eye rays at random...
All effects of the eye rays are magical, so they would be suppressed. To be clear, "suppressed" in this context means that those effects disappear inside the area of effect, but aren't removed. They will return as soon as the area is left.