We discuss a bijection between the Z_k parafermions CFT quasi-particle basis and the RSOS lattice paths. This bijection also implies a bijection between Bressoud lattice paths and RSOS lattice paths. We generalize this result for the graded parafermionic models and use it to construct a new fermionic character formula for the M(k+1,2k+3) minimal models, which are dual to the graded parafermions.