Vortex dynamics in superconductors have received a great deal of attention from both fundamental and applied researchers over the past few decades. Because of its critical role in the energy relaxation process of type-II superconductors, vortex dynamics have been deemed a key contributor to the response rate of the emerging superconducting single photon detector (SSPD). With the support of electrical transport measurements under external magnetic fields, vortex dynamics in superconducting a-MoSi thin films are investigated in this work. It is ascertained that the vortex state changes from pinned to flux flow under the influence of the Lorentz force. The critical vortex velocity v* and quasi-particle inelastic scattering time {tau}* under different magnetic fields are derived from the Larkin-Ovchinnikov model. Under high magnetic fields, the v* power law dependence (v*~B-1/2) collapses, i.e., v* tends to zero, which is attributed to the obstruction of flux flow by the intrinsic defects, while the {tau}* increases with the increasing magnetic field strength. In addition, the degree of vortex rearrangement is found to be enhanced by photon-induced reduction in potential barrier, which mitigates the adverse effect of film inhomogeneity on superconductivity in the a-MoSi thin films. The thorough understanding of the vortex dynamics in a-MoSi thin films under the effect of external stimuli is of paramount importance for both further fundamental research in this area and optimization of SSPD design.