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The paper introduces a new class of convexity named strongly modified (p, h)-convex functions and establishes various properties of these functions, providing a comprehensive understanding of their behavior and characteristics. Additionally, the paper investigates Schur inequality and Hermite-Hadamard (H-H) inequalities for this new class of convexity. Also, H-H inequalities are proved within context of Riemann-Liouville integrals and Caputo Fractional derivatives. The efficiency and feasibility of Schur inequality and H-H inequalities are supported by incorporating multiple illustrations, that demonstrate the applicability of strongly modified (p, h)-convex functions. The results contribute to the field of mathematical analysis and provide valuable insights into the properties and applications of strongly modified (p, h)-convex functions., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2024 Nosheen et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)