Recently, a new type of set-valued mapping called soft set-valued map was introduced in the literature as a generalization of the concepts of fuzzy set-valued and multi-valued mappings. This present article extends the new notion by establishing, among others, the idea of common $e$-soft fixed point of soft set-valued maps. From application point of view, one of our obtained results is employed to establish novel sufficient conditions for the existence of fuzzy number-valued solution of fuzzy Volterra integral equation. Non-trivial examples are further provided to support the hypotheses of our results. The presented idea herein includes several fixed point theorems on point-to-point and point-to-set valued mappings as consequences. A few of these special cases are highlighted and discussed.