A special subset of generalized fractional superstring models extending those of Argyres et al is studied. This subset concerns models based on SU_K (K )/U (1)^{K -1} Gepner parafermions. It is shown that there exists a remarkable link between generalized fractional superstrings based on SU_K (K )/U (1)^{K -1} Wess-Zumino-Witten theory with K = 2, 3 and 5, and the associative division algebras. These models have critical dimensions 10, 2 × 5 and 4 × 3, respectively, and are in one-to-one correspondence with real, Kähler, and hyper-Kähler target spaces. Moreover, we obtain field-theoretical realizations of c ₀ = 4 super-W ₃ and c ₀ = 12 super-W ₅ symmetries based on the K = 3 and 5 parafermions. It is also shown that the conformal anomaly of the parafermion ghosts of the worldsheet fractional supersymmetry is C_paraghost = 15 - K ² .