<p>This study presents a novel higher-order shear deformation theory, integrated with the modified couple stress theory, to investigate, for the first time, size-dependent effects in functionally graded triply periodic minimal surface (FG-TPMS) microbeams. The proposed model employs the Gegenbauer polynomial to capture shear deformation while rigorously enforcing vanishing shear stresses at the upper and lower beam surfaces. Three representative TPMS architectures—Primitive, Gyroid, and I-Wrapped Package Graph—are analysed. The governing equations are derived via Lagrange’s principle and solved using the Ritz method, with shape functions constructed from Gegenbauer polynomials. Numerical simulations are conducted to validate the theoretical predictions against analytical solutions and to examine the influence of size effects on bending, buckling, and free vibration responses of FG-TPMS microbeams. The findings demonstrate that the proposed theory provides a simple yet robust framework for accurately characterising the mechanical behaviour of FG-TPMS microbeams.</p>