A Lorentz-invariant gauge theory for massive fermions on R × S 3 spacetime is built up. Using the symmetry of S 3,we obtain Dirac-type equation and derive the expression of the fermionic propagator. Finally, starting from the SU(N) gauge-invariant Lagrangian, we obtain the set of Dirac-Yang-Mills equations on R × S 3 spacetime, pointing out major differences from the Minkowskian case.