Here's a suggestion for how the threaded two rotation coil version of Podkletnov's apparatus works. A diagram of the coil arrangement is shown below. Only one of the coils is shown in the diagram. The second coil is a mirror image of the first on the right side of the disc.
The magnetic field, (B coil), created by the coil will be parallel to the surface of the superconducting disc. Via the Meissner effect, supercurrents will be setup in the superconductor that are parallel to the coil windings, but in the opposite direction. These supercurrents are at right angles to the magnetic field that originally created them. The magnetic field, (B supercurrent), setup by the supercurrents opposes the magnetic field in the rotation coil, (see figure below). If the two rotation coils are driven by alternating currents that are 180 degrees out of phase, then the opposing magnetic fields setup by the superconductor should create a net torque on the disc.
Meissner Effect on Wikipedia