  Unequivocal signatures of Majorana zero energy modes in condensed matter
systems and manipulation of the associated electron parity states are highly
sought after for fundamental reasons as well as for the prospect of topological
quantum computing. In this Letter, we demonstrate that a ring of Josephson
coupled topological superconducting islands threaded by magnetic flux and
attached to a quantum dot acts as an excellent parity-controlled probe of
Majorana mode physics. As a function of flux threading through the ring,
standard Josephson coupling yields a $\Phi_0=h/(2 e)$ periodic features
corresponding to $2\pi$ phase difference periodicity. In contrast, Majorana
mode assisted tunneling provides additional features with $2\Phi_0$ ($4\pi$
phase difference) periodicity, associated with single electron processes. We
find that increasing the number of islands in the ring enhances the visibility
of the desired $4\pi$ periodic components in the groundstate energy. Moreover
as a unique characterization tool, tuning the occupation energy of the quantum
dot allows controlled groundstate parity changes in the ring, enabling a
toggling between $\Phi_0$ and $2\Phi_0$ periodicity.
