  The detection of the Majorana bound states (MBSs) is a central issue in the
current investigation of the topological superconductors, and the topological
Josephson junction is an important system for resolving this issue. In this
work, we introduce an external quantum dot (QD) to Majorana Josephson junctions
(MJJs), and study the parity flipping of the junction induced by the coupling
between the QD and the MBSs. We demonstrate Landau-Zener (LZ) transitions
between opposite Majorana parity states when the energy level of the QD is
modulated. The resulted parity flipping processes exhibit voltage signals
across the junction. In the presence of a periodic modulation on the QD level,
we show Landau-Zener-St\"{u}ckelberg (LZS) interference on the parity states.
We demonstrate distinctive interference patterns at distinct driving
frequencies. These results can be used as signals for detecting the existence
of the MBSs.
