The electronic currents and magnetic fields generation of H65+and H43+ molecules with current-carrying states by circularly polarized (CP) and linearly polarized (LP) laser pulses are investigated. Results show that the electronic currents and magnetic fields induced by the CP pulse are higher than those by the LP pulse for both molecules in resonance excitation scheme. It can be attributed to the switchable dipole moment by the laser pulses, inducing selective state-to-state electronic transitions. Moreover, it was found that magnetic fields are sensitive to different initial states of molecules in ionization scheme. Especially, the magnetic fields induced by the current-carrying states are much higher than that by the ground state, which is because the current-carrying state has stable electronic ring current, and the magnetic field induced by it is contributed by the current-carrying state itself and the laser field. These findings provide a scheme for generating ring-shape currents and magnetic fields in molecular systems for future researches in ultrafast magneto-optics.