  We study the behavior of a topological Josephson junction in which two
topological superconductors are coupled through a quantum dot. We focus on the
case with the bulk superconducting gap being the largest energy scale. Two
parameter regimes are investigated: a weak tunneling between the dot and the
superconductors, with the dot near its charge degeneracy point, and a strong
tunneling regime in which the transmission between the dot and the
superconductors is nearly perfect. We show that in the former situation, the
Andreev spectrum for each sector with fixed fermion parity consists of only two
levels, which gives rise to the nontrivial current-phase relation. Moreover, we
study the Rabi oscillation between the two levels and indicates that the
corresponding frequency is a $4\pi$-periodic function of the phase difference
between the two superconductors, which is immune to the quasiparticle
poisoning. In the latter case, we find that the Coulomb charging energy
enhances the effect of backscattering at the interfaces between the dot and the
superconductors. Both the temperature and the gate-voltage dependence of the
critical Josephson current are examined.
