Edge states in narrow quasi two-dimensional nanostructures determine to large extent electric, thermoelectric and magnetic properties. Non-magnetic edge states may quite often lead to the topological insulator type behavior. However another scenario develops when the zigzag edges are magnetic and the time reversal symmetry is broken. In this work we report on electronic band structure modifications, electrical conductance and thermoelectric properties of narrow zigzag nanoribbons with spontaneously magnetized edges. Theoretical studies based on the Kane-Mele-Hubbard tight-binding model show that for silicene, germanene and stanene both the Seebeck coefficient and the thermoelectric power factor are strongly enhanced for energies close to the charge neutrality point. Perpendicular gate voltage lifts spin-degeneracy of energy bands in the ground state with antiparallel magnetized zigzag edges, and makes the electrical conductance significantly spin-polarized. Simultaneously the gate voltage worsens the thermoelectric performance. Estimated room-temperature figures of merit for the aforementioned nanoribbons can exceed a value of 3 if phonon thermal conductances are adequately reduced.