We present analytic formula for the differential cross section (DCS) of the antineutrino–electron scattering (AES) in a magnetic field (MF) with allowance for the longitudinal polarizations of the initial and final electrons, analyze polarization effects and show possible applications of the obtained results. The DCS of AES in MF is sensitive to the spin variable of the initial and final electrons and to the direction of the incident and scattered antineutrinos. Spin asymmetries and field effects in AES in MF enable us to use initial electrons with right-hand circular polarization (RHCP) as polarized electron targets in detectors for detection of antineutrinos of low energy or relic antineutrinos, and for distinguishing antineutrino flavour. In general, the gas consisting of the electrons having a left-hand circular polarization (LHCP) and the gas consisting of the electrons having RHCP are heated by antineutrinos asymmetrically. The asymmetry of heating is sensitive to the antineutrino flavour. In the heating process of electrons by antineutrinos the dominant role belongs to electron antineutrinos compared with the contribution of muon (tauon) antineutrinos. In AES in a MF, electrons with LHCP are heated by , and equally when both the initial and final antineutrinos fly along or against MF direction. Electrons with RHCP in AES in a MF are heated by and unequally when both the initial and final antineutrinos fly along or against MF direction.