Accurate measurements of electron and positron fluxes in the energy range 0.2–10 GeV have been performed with the Alpha Magnetic Spectrometer (AMS) at altitudes of 320–390 km in the geographic latitude interval ±51.7°. We focus on the fluxes measured in the regions nearby the South Atlantic Anomaly, defined by the local magnetic values of the magnetic field B (0.21 ≤ B ≤ 0.26 G) at the altitude of AMS. A clear transition from the Stably Trapped population typical of the Inner Van Allen belts to Quasi‐Trapped population in the regions underneath the Van Allen belts is observed. The high energy observations demonstrate the relatively higher abundance of positrons in the Inner Van Allen belts, for both the Stably Trapped and the Quasi‐Trapped populations. The flux maps as a function of the canonical adiabatic variables L, αo are presented for the interval 0.95 < L < 3, 0° < αo < 90° for electron energies below 10 GeV and positrons energies below 3 GeV. The results are compared with existing data at lower energies.