Supersymmetry formulation of the classical action of interacting charged and neutral fermions with arbitrary value of the anomalous magnetic moment is considered. This formulation generalize the well-known action for scalar charged particles which was considered in works of Fokker, Schwartzshild, Tetrode, Willer and Feyman. The super-field formulation of electrodynamics of the Maxwell super-multiplet built out of the space coordinates of charged and neutral fermions is obtained from the given action. The new field theoretical minimumality condition, which allows to describe in the usual way the standard Pauli minimum and non-minimum fermion interaction with the electromagnetic field, is proposed as the consequence of the considered formulation.