The spatial homogeneity and temporal stability of a fountain clock’s quantized axial magnetic field are essential factors that govern frequency stability and uncertainty. In this study, the quantized axial magnetic field system of a transportable rubidium fountain atomic clock is constructed and optimally designed considering several aspects, such as external magnetic field shielding, magnetic field coil design, and coil current source stability. A five-layer permalloy magnetic shield is used to shield the external magnetic field to eliminate the influence of the ambient magnetic field on the quantized axial magnetic field. The appropriate current is obtained through simulation using four groups of symmetrical compensation coils. The fluctuation of magnetic field less than 1 nT is obtained in a 30-cm free flight trajectory of the cold atoms cloud. The temporal stability of the quantized axial magnetic field is optimized by improving the C-field supply current method, and the fluctuation of the field over time is less than 0.1 nT. After optimization, the long-term frequency stability of the fountain clock reaches 2.9×10^-16, and the uncertainty of the second-order Zeeman frequency shift caused by the inhomogeneity of the magnetic field spatial distribution is less than 3.4×10^-19. Additionally, the uncertainty of the second-order Zeeman frequency shift caused by the fluctuation of the magnetic field with time is approximately 5.1×10^-17.