Using exact diagonalization methods we study possible phases in a one-dimensional model of two differently populated fermionic species in a periodically driven optical lattice. The shaking amplitude and frequency are chosen to resonantly drive s−p transition while minimizing the standard intraband tunnelings. We verify numerically the presence of an emergent density wave configuration of composites for appropriate filling fraction and minimized intraband tunnelings. The majority fermions moving in such a lattice mimic the celebrated Rice-Mele model. Far away from that region, the structure changes to a clustered phase, with the intermediate phase abundantly populated by defects of the density wave. These defects lead to localized modes carrying fractional particle charge. The results obtained are compared with earlier approximate predictions.