Electron polarization induced by magnetic fields can modify the potentials relevant for describing neutrino conversions in media with magnetic fields. The magnitudes of polarization potentials are determined for different conditions. We show that variations of the electron polarization along the neutrino trajectory can induce resonant conversions in the active-sterile neutrino system, but cannot lead to level crossing in the active-active neutrino system. For neutrino flavour conversions the polarisation leads only to a shift of the standard MSW resonance. For polarizations $\lambda \lsim 0.04$ the direct modifications of the potential (density) due to the magnetic field pressure are smaller than the modifications due to the polarization effect. We estimate that indeed the typical magnitude of the polarization in the sun or in a supernova are not expected to exceed 10−2. However even such a small polarization may lead to interesting consequences for supernova physics and for properties of neutrino signals from collapsing stars.