We study asymmetric excitations of toroidal dipole resonance and magnetic dipole quasi-bound state in the continuum (BIC) in hybrid graphene-dielectric metasurface consisting of a nanoring and a Y-shaped nanobar. Through reducing or increasing inner radius of nanoring, the quasi-BIC dominated by magnetic dipole moment can be excited and effectively modulated via adjusting the Fermi energy and layer numbers of the graphene. The proposed metasurface can not only produce a symmetric localized magnetic field distribution but also create two asymmetric localized magnetic field distributions in near-infrared wavelength, providing a new way of indirectly manipulating the localized magnetic field enhancement. Our results can be of practical interest for a variety of applications including optical modulator, filter, switches and light trapping.