In this article, taking advantage of the special magnetic shieldings and the optimal coil design of a transportable Rb atomic fountain clock, the intensity distribution in space and the fluctuations with time of the quantization magnetic field in the Ramsey region were measured using the atomic magneton-sensitive transition method. In an approximately 310 mm long Ramsey region, a peak-to-peak magnetic field intensity of a 0.74 nT deviation in space and a 0.06 nT fluctuation with time were obtained. These results correspond to a second-order Zeeman frequency shift of approximately $(2095.5\pm 5.1)\times {10}^{-17}$. This is an essential step in advancing the total frequency uncertainty of the fountain clock to the order of ${10}^{-17}$.