  Parafermion zero modes can be trapped in the domain walls of quantum Hall
edges proximitized by superconductors and ferromagnets. The $\nu = 1/3$
fractional quantum Hall side strip arising due to edge reconstruction of a $\nu
= 1$ edge doubles the number of topological sectors such that each of them is
$Z_{2} \times Z_{2}$ degenerate. The many-body spectrum displays a $4\pi$
Josephson periodicity, with the states in each $Z_{2}$ being energetically
decoupled. Signatures of the new states appear in the fractional Josephson
current when the edge velocities are taken to be different.
