For an epitaxial film of an electron-doped superconductor \({\text{Nd}}_{2-x}{\text{Ce}}_{x }{\text{CuO}}_{4}\) (x = 0.145), in a mixed state, a well-defined step structure is observed on the dependence of the c-axis resistance on the magnetic field parallel to CuO2 layers. It is shown that in the region of the free flow of Josephson vortices, an exponential dependence of monotonous \({R}_{c}(B)\) component in the flux-flow mode is observed. The "quantized" steps of equal height in the actual range of magnetic fields were registered with a period of \(\Delta B\sim {\Phi }_{0}/\left({\lambda }_{ab}{\lambda }_{c}\right)\) where the magnetic penetration depths in the ab-plane ( \({\lambda }_{ab}\) ) and along the c-axis ( \({\lambda }_{c}\) ) determine the sizes of the Josephson vortices in anisotropic layered superconductor. We associate the periodic steps of magnetoresistance with the resonant response of the system under study to the magnetic field-induced change in the number of Josephson vortices, each of which contains a magnetic flux quantum.
