We investigate the control mechanisms of single-photon scattering in a hybrid system consisting of superconducting qubits coupled to an SSH (Su-Schrieffer-Heeger) topological photonic lattice under the influence of an artificial gauge field. This research is driven by the growing interest at the intersection of quantum optics and condensed matter physics, particularly in the realm of topological quantum optics, where the robustness of photon transport against defects and impurities can be exploited for quantum information processing. To achieve this, we develop a theoretical model that incorporates the phase of the artificial gauge field into the coupling between superconducting qubits and the SSH photonic lattice. Using the probability-amplitude method, we analytically derive expressions for the reflection and transmission amplitudes of single photons. Our results show that the artificial gauge field can effectively control single photon scattering in both the upper and lower energy bands of the SSH lattice, enabling total transmission in the upper band and total reflection in the lower band. This band-dependent scattering behavior exhibits a high degree of symmetry with respect to the lattice momentum and energy bands. Importantly, the reflection coefficient can be made independent of the lattice coupling strength and depends solely on the topological properties of the lattice. This finding suggests a robust method for detecting topological invariants in photonic lattices. Furthermore, we extend our analysis to various coupling configurations between superconducting qubits and the photonic lattice, highlighting the versatility of the artificial gauge field in manipulating photon transport. These findings not only provide new insights into the control of photon transport in topological photonic lattices but also open the door to the development of novel quantum optical devices and robust quantum information processing platforms.