A novel class of generalized strongly modified (GSM) $ (p, h) $-convex functions (CFs) was presented in paper and its fundamental properties were established. Schur, Hermite-Hadamard (H-H), and Fejér inequalities were proved for this new notion of convexity. Several illustrations have been incorporated by selecting several GSM $ (p, h) $-CFs to substantiate the existence and feasibility of Schur, H-H, and Fejér-type inequalities. These inequalities are valuable resources for analyzing the characteristics of newly defined GSM $ (p, h) $-CFs. A comparison was given to show that the results of this study represent a significant improvement over those of earlier publications.