  We study theoretically a junction of a $\mathcal{PT}$-symmetric non-Hermitian
superconductor (PTS) placed between two conventional superconductors. We show
that due to non-Hermitian electron-electron interaction in the PTS region and
the combination of symmetries, only discrete values of phases of the
conventional superconductors yield solutions for Andreev bound states.
Remarkably, in the case of $0$ and $\pi$, we obtain growing and decaying in
time Andreev bound states. For $\pi/2$ and $3\pi/2$, there is a Majorana zero
mode penetrating through the junction in only one direction forming a
quasiparticle supercurrent.
