  We study analytically a current-biased topological Josephson junction
supporting $\mathbb{Z}_n$ parafermions. First, we show that in an infinite-size
system a pair of parafermions on the junction can be in $n$ different states;
the $2\pi{n}$ periodicity of the phase potential of the junction results in a
significant suppression of the maximal current $I_m$ for an insulating regime
of the underdamped junction. Second, we study the behaviour of a realistic
finite-size system with avoided level crossings characterized by splitting
$\delta$. We consider two limiting cases: when the phase evolution may be
considered adiabatic, which results in decreased periodicity of the effective
potential, and the opposite case, when Landau-Zener transitions restore the
$2\pi{n}$ periodicity of the phase potential. The resulting current $I_m$ is
exponentially different in the opposite limits, which allows us to propose a
new detection method to establish the appearance of parafermions in the system
experimentally, based on measuring $I_m$ at different values of the splitting
$\delta$.
