: Search for Non-Abelions - particles whose exchange transforms the quantum state of a system noncommutatively - is driven both by the quest for deeper understanding of nature and prospects for universal topological quantum computation. Examples of non-Abelions are Majorana and parafermion zero modes. Most of current research is aimed at Majorana qubits, but the set of topologically protected operations with Majorana qubits is limited. Braiding of parafermion modes can produce a richer set of such operations. However, physical systems that can host these exotic excitations are rare and hard to realize in experiments. I will describe an example of such feasible system: the domain wall formed in spin transitions between spin-polarized and spin-unpolarized phases of the fractional quantum Hall effect.  There are signatures of topological superconductivity in numerical modeling of proximity coupling of an s-type superconductor to the domain wall at the boundary between two fractional quantum Hall liquids, where helical fractional quantum Hall modes with opposite spin propagate in opposite directions. We show that this leads to emergence of parafermions. While Majorana zero modes form a double degenerate state, parafermions emerge as a six-fold degenerate state. In electron systems, spin transitions in fractional Quantum Hall effect in GaAs have been experimentally observed at a filling factor 2/3. We will describe analytic and numerical approaches to domain walls in the fractional quantum Hall system. To describe experimental data, we developed theory of tunneling of Luttinger modes through the domain wall of a finite length and analyzed the role of nuclear spins in this system.