A new model of the internal structure of certain types of celestial bodies is proposed. It is based on the concept that some neutron stars might have been formed earlier than all other type of stars, at an early stage of expansion of the universe, directly from continuous cosmic matter. Under such conditions, a neutron star after forming becomes an efficient center for the accretion of cosmic plasma. The plasma streams falling onto the neutron star carry magnetic fields with them that are created in the process (by thermoelectric currents and the dynamo process) and pack the fields tightly around the star. After a certain time, an extended and strongly magnetized plasma layer is formed around the neutron star. As a result, a stellar configuration is formed with an outer layer, mass, radius, and luminosity similar to those of an ordinary star. In the magnetized part of such a configuration, the gravitational attraction of the masses is compensated for by a magnetic pressure gradient, while the plasma is confifned by the magnetic field itself. Numerical estimates corroborate the possibility that magnetized stars exist. The radii and masses of the magnetized spheres of such stars are considerably less than the radii and masses of the corresponding configurations, so in observations they should not differ from ordinary stars: the outer layers (intermediate layer, photosphere, and chromosphere) of the magnetized configuration are the same as for an ordinary star. Structural differences may appear in the inner regions, however, involving magnetic activity and neutrino luminosity, for example.