Under the influence of an external magnetic field and spin-changing collisions, the band insulator state of one-dimensional $s$-wave repulsively interacting four-component fermions at half-filling transforms into Mott insulator states with a spontaneously doubled unit cell: a dimerized state for shallow lattices and a N\'eel state for deep lattices via an intermediate topological state. These Mott insulator phases could be of special interest for experiments as they can be reached starting from band insulator state and changing magnetic field adiabatically.