  We propose a disc-corona model in which a geometrically thin, optically thick
disc surrounds a Kerr black hole, and magnetic fields exert a time-steady
torque on the inner edge of the accretion disc. The analytical expression of
the total gravitational power is derived from the thin-disc dynamics equations
by using this new boundary condition. It is shown that the magnetic torque can
considerably enhance the amount of energy released in the disc-corona system.
Furthermore, the global solutions of this disc-corona system are obtained
numerically. We find that the fraction of the power dissipated into the corona
in the total for such disc-corona system increases with the increasing
dimensionless black hole spin parameter $a_\ast $, but is insensitive on the
$\Delta \varepsilon $ which is the additional radiative efficiency parameter
relevant to magnetic torque, for $\Delta\varepsilon > 1$. In addition, the
emerged spectra from this disc-corona system are simulated by using Monte-Carlo
method, and the effect of the different parameters on the output spectra is
discussed.
