The mechanism of controlling single-photon scattering in a hybrid system consisting of superconducting qubits coupled to a Su-Schrieffer-Heeger (SSH) topological photonic lattice is investigated under the influence of an artificial gauge field. This research is driven by the growing interest in the intersection between quantum optics and condensed matter physics, particularly in the field of topological quantum optics, where the robustness of photon transport against defects and impurities can be used for quantum information processing. To achieve this, a theoretical model, which incorporates the phase of the artificial gauge field into the coupling between superconducting qubits and the SSH photonic lattice, is developed in this work. The analytical expressions for the reflection and transmission amplitudes of single photons are derived by using the probability-amplitude method. The results show that the artificial gauge field can effectively control single photon scattering in both the upper energy band and the lower energy band of the SSH lattice, thereby 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 dependent solely on the topological properties of the lattice. This finding suggests a robust method of detecting topological invariants in photonic lattices. Furthermore, our analysis is extended 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.