We study a parafermion Josephson junction comprising a pair of counterpropagating edge modes of two quantum Hall systems, proximitized by an $s$-wave superconductor. We show that the difference between the lengths (which can be controlled by external gates) of the two counterpropagating chiral edges at the Josephson junction, can act as a source of spontaneous phase bias. For the Laughlin filling fractions, $\nu =1/m, m\in 2\mathbb{Z}+1$, this leads to an electrical control of either Majorana ($m=1$) or parafermion ($m\ne 1$) zero modes.

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• Edge states
• Electrical conductivity
• Landau levels
• 1-dimensional systems
• Josephson junctions
• Bogoliubov-de Gennes equations
• Bosonization
• Non-Abelian models
• S-matrix method in transport