The Making of Star Trek
, written during the second season of TOS, clearly identifies the parabolic dish of the ship as "main sensor-deflector" (not in the Jefferies drawing but in the text description).
And in the third season ("The Paradise Syndrome") they featured the (unconventional?) use of the main deflector to deflect
the asteroid to alter its course (before Spock applies the "diamond-cutting" Plan B to destroy the asteroid by phasers).
Therefore I have little doubt that the phaser beam in TOS (in contrast to TOS-R) emanated from the parabolic dish.