This is a preprint of a theoretical study in statistical mechanics. We propose a generalized statistical framework based on para-statistics,introducing a modified grand partition function and generalized distributionfunctions. The formulation systematically extends conventional Bose–Einsteinand Fermi–Dirac statistics. This work is independent of the authors’ previously published studies andpresents a new theoretical framework. This preprint is intended for submission to arXiv in the category ofstatistical mechanics.