Ramond and Neveu-Schwarz paraspinning strings in presence of D-branes

We investigate the theory of an open parafermionic string between two parallel Dp-, Dq-branes in Ramond and Neveu-Schwarz sectors. Trilinear commutation relations between the string variables are postulated and the corresponding ones in terms of modes are derived. The analysis of the spectrum shows that one can again have a free tachyon Neveu-Schwarz model for some values of the order of the paraquantization associated to some values of p and q. The consistency of this model requires the calculation of the partition function and its confrontation with the results of the degeneracies. A perfect agreement between the two results is obtained and the closure of the Virasoro super-algebra is confirmed.