Intraocular muscle supplied by Edinger Westphal nucleus is

All pas of the muscle are supplied by parasympathetic nerves. The pathway involves the Edinger-Westphal nucleus, oculomotor nerve, and the ciliary ganglion. The nerve to inferior oblique gives a branch for the ciliary ganglion. This branch brings the fibres of Edinger-Westphal nucleus (GVE) to the ganglion for relay. The postganglionic fibres end up in supplying the ciliaris for enhancing the anterior curvature of the lens and the sphincter pupillae for narrowing the size of the pupil. Both these are intraocular muscles required for accommodation. Ref: BD Chaurasia's HUMAN ANATOMY, Volume 3, 4th edition