The experimental search for non-abelian anyons has extended beyond that of Majorana modes with advances in the understanding, manipulation and construction of fractional quantum Hall systems and their combination with elements like superconductors. Further fractionalisation of the electron degrees of freedom leads to parafermionic modes that can share fractions of the elementary charge non-locally. In this thesis we study the Z6 parafermions through transport spectroscopy and find that their fractional degree of freedom can be observed from a current readout via a standard metallic electrode. By simulating the dynamics of an open quantum system of two parafermions, we show that interaction with a fractional quantum Hall environment, causing fractional quasiparticle poisoning of the parafermion charge, reveals itself in a two or three-level telegraph noise in the current. To this end we use the stochastic quantum jump method and extend the jump operator formalism to describe fractional charges. Finally, we propose and study a protocol to experimentally verify the fusion algebra in a construction with four parafermions. In conclusion, the thesis presents proposals and indications for future experiments to measure compelling signatures of parafermionic modes.