Abstract Three solar energetic particle (SEP) events originating from solar active region 13664 occurred on 10–16 May 2024, coinciding with a geomagnetic superstorm. Using data from the Geostationary Operational Environmental Satellites and Meteorological Operational satellite‐C, we investigate the energetic proton fluxes and east‐west flux ratios in geostationary orbit, as well as the cutoff L $L$‐shells measured in low Earth orbit during these events. For the first time, we find the rigidity dependence of the correlations between the east‐west proton flux ratios and the Kp $Kp$ index, the Dst $Dst$ index, and solar wind dynamic pressure. The corresponding correlation coefficients significantly increase and then decrease with the increase of proton rigidity. Such non‐monotonic variation can be well explained by the penumbral rigidity cutoffs of penetrating protons in west‐looking and east‐looking directions. The results suggest the strong influence of geomagnetic shielding on SEP penetration.