Parafermions are generalizations of Majorana fermions that may appear in interacting topological systems. They are known to be powerful building blocks of topological quantum computers. Existing proposals for realizations of parafermions typically rely on strong electronic correlations which are hard to achieve in the laboratory. We identify a novel physical system in which parafermions generically develop. It is based on a quantum constriction formed by the helical edge states of a quantum spin Hall insulator in the vicinity of an ordinary s-wave superconductor. Interestingly, our analysis suggests that Z_{4} parafermions are emerging bound states in this setup in the weakly interacting regime. Furthermore, we identify a situation in which Majorana fermions and parafermions can coexist.