This paper explored the optically induced magnetization properties of radially polarized Bessel-Gaussian vortex beams with radial phase modulation in a 4π high numerical aperture (NA) focusing system, which is based on the vector diffraction theory and the inverse Faraday effect. The results show that in the case of radial modulation parameter L=0, one longitudinal magnetization chain with adjustable length can be obtained by modulating the truncation parameter β. When the radial modulation parameter L=1.3, two magnetization chains can be obtained by modulating the truncation parameter β. By modulating the radial modulation parameter L, two magnetization chains along the optical axis can be generated, each with four dark magnetic traps; meanwhile, the spacing between two magnetization chains can be adjusted. These results may be helpful in high-density all-optical magnetic recording, atom capture, and magnetic resonance microscopy.