This study assesses the performance of several shear connectors—specifically I-shaped, Angle, Channel, and Stud connectors—in steel–concrete composite H-beam sections by Finite Element Analysis (FEA) in Abaqus, according to Eurocode 4 standards. The numerical models explore slip behaviour, strain distribution, and deflection characteristics under push-out loading conditions. The results indicate that the I-connector had the greatest shear capacity of 454.56 kN with a typical slip of 9.71 mm, indicating strong yet comparatively brittle behaviour. The Channel connector provided a balanced response, attaining 428.93 kN with a slip of 12.51 mm. Conversely, the Angle and Stud connections exhibited superior ductility, with typical slips of 13.68 mm and 14.09 mm, respectively, despite lower peak loads. The results demonstrate the influence of shear connector types on the overall structural behavior, enabling a comparative assessment of their effectiveness. This research contributes to the optimization of composite beam designs, offering practical recommendations for improving the structural efficiency and serviceability of steel–concrete composite systems.