We use two-dimensional high-resolution MHD simulations to investigate the effects of magnetic fields on the formation and evolution of such substructures as well as on the mass inflow rates to the galaxy center. We find that there exists an outermost x1-orbit relative to which gaseous responses to an imposed stellar bar potential are completely different between inside and outside. Inside this orbit, gas is shocked into dust lanes and infalls to form a nuclear ring. Magnetic fields are compressed in dust lanes, reducing their peak density. Magnetic stress removes further angular momentum of the gas at the shocks and leads to a smaller and more centrally distributed ring, resulting in the mass inflow rates larger, by more than two orders of magnitude, than in the unmagnetized counterparts. Outside the outermost x1-orbit, on the other hand, an MHD dynamo operates near the corotation and bar-end regions, efficiently amplifying magnetic fields. The amplified fields shape into trailing magnetic arms with strong fields and low density. The base of the magnetic arms have a thin layer in which magnetic fields with opposite polarity reconnect via a tearing-mode instability. This produces numerous magnetic islands with large density which propagate along the arms to turn the outer disk into a highly chaotic state.