Let {X(t) : t $geq$B 0} be a Symmetric $alpha$ Stable and H-Self-similar process with stationary increments. We examine a.s. Holder unboundedness of S$alpha$S H-sssi Chentsov processes and H-sssi Chentsov fields for order ${gamma}$>H. Finally, we prove a.s. Holder continuity of S$alpha$S H-sssi processes with ergodic seating transformations for the case of H>1/$alpha$.