  We theoretically report the emergence of $Z_4$ parafermion edge modes in a
periodically driven spinful superconducting chain with modest fermionic Hubbard
interaction. These parafermion edge modes represent $\pm \pi/(2T)$ quasienergy
excitations ($T$ being the driving period), which have no static counterpart
and arise from the interplay between 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.
