Statement - (A) : A steady current is flowing in a cylindrical conductor, the electric field with in the conductor is not zero.
Statement - (B) : Electrons in a conductor have no motion in the absence of a potential difference across it.

Electric field exists within the conductor because it is the electric field which imparts acceleration to electrons for the flow of current.

The electrons move inside the conductor in a random manner even when there is no potential difference applied across the conductor.