In this paper we develop the necessary tools to generalize the function spaces F(p,q,s) and F0(p,q,s) introduced by Zhao in [Zha] to the case of the monogenic functions defined in the unit ball of R3.Obtaining at the same time the generalization of Qp monogenic spaces presented in [GuKaShTo] and Bq;p monogenic spaces in [ElGuReTo].