Not sure what effect you’re after - I downloaded your demo scene, which was very basic with a sphere rotating around, but no textures or materials at all.
What I gather is that you want to show material of Ring on one side of the sphere, and transparent on the other side? If that’s the case, UV map a black/white image to the ring, line up the black/white transition point to the sphere (or likely on the seam), then parent the ring to the sphere so it follows.