Steel–concrete composite decks are commonly employed in narrow-width steel box composite girder bridges to augment their lateral spanning capabilities, while the concurrent omission of longitudinal stiffeners leads to a substantial reduction in the number of components, thereby yielding a structurally optimized bridge configuration. This paper delineates the structural design parameters of a narrow-profile steel box composite girder bridge and assess the mechanical behavior of its incorporated steel–concrete composite deck under static and fatigue loading conditions. To this end, two full-scale segment specimens from the composite bridge decks were subjected to equal amplitude cyclic fatigue tests. The investigation specifically concentrated on the impacts of two types of shear connectors—namely, perforated steel plates combined with shear studs and perfobond rib shear connectors (PBL connectors)—on the static and fatigue performance, including fatigue stiffness, of the steel–concrete composite bridge decks. The results indicate that, under the static bending condition, the composite deck specimen equipped with stud connectors demonstrates superior overall flexural stiffness in comparison to the specimen featuring PBL connectors. Furthermore, the flexural stiffness of the steel–concrete composite specimens experiences a negligible alteration across two million fatigue loading cycles. Upon the completion of two million fatigue loading cycles, the composite deck specimens incorporating the shear connectors composed of perforated steel plates and shear studs exhibit relatively wider crack widths under the static peak load. Both configurations of the steel–concrete composite bridge deck specimens manifest evident interfacial detachment, signifying insufficient tensile pull-out stiffness of the shear connectors. It is recommended to increase the quantity of the shear connectors or select the pertinent types in order to enhance the interface shear resistance.