How to rotate an object in certain angle with respect to its parent

I am trying to rotate this circular disc along the side of the cube.

But when the cube is tilted, it gets hard for the circular disc to rotate along the cubes side. It gets inside it.

I have tried rotating the circular disc with the 'cube.normal' and also with the normal '(disc.transform.position - cube.transform.position)' in disc.transform.rotate(Vector3, space.world). Both of these gets the circular disc inside the cube as shown in the figure.

Can someone help me out in order to stick the circular disc to the cube and rotate. (left and right)