We theoretically report the emergence of $Z_4$ parafermion edge modes in a periodically driven spinful superconducting chain with a modest fermionic Hubbard interaction. These parafermion edge modes represent $\pm \pi /\left(2T\right)$ quasienergy excitations ($T$ being the driving period), which have no static counterpart and arise from the interplay between an interaction effect and periodic driving. At special parameter values, these exotic quasiparticles can be analytically and exactly derived. Strong numerical evidence of their robustness against variations in parameter values and spatial disorder is further presented. Our proposal offers a route toward realizing parafermions without fractional quantum Hall systems or complicated interactions.

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• Majorana fermions
• Parafermions
• Topological superconductors
• Floquet systems
• Strongly correlated systems