  Fractional quantum Hall-superconductor heterostructures may provide a
platform towards non-abelian topological modes beyond Majoranas. However their
quantitative theoretical study remains extremely challenging. We propose and
implement a numerical setup for studying edge states of fractional quantum Hall
droplets with a superconducting instability. The fully gapped edges carry a
topological degree of freedom that can encode quantum information protected
against local perturbations. We simulate such a system numerically using exact
diagonalization by restricting the calculation to the quasihole-subspace of a
(time-reversal symmetric) bilayer fractional quantum Hall system of Laughlin
$\nu=1/3$ states. We show that the edge ground states are permuted by
spin-dependent flux insertion and demonstrate their fractional $6\pi$ Josephson
effect, evidencing their topological nature and the Cooper pairing of
fractionalized quasiparticles.
