  In this paper, we study the magnetic reconnection process of energy
extraction from a rapidly rotating Kerr-Newman-modified-gravity (MOG) black
hole by investigating the combined effect of black hole charge and the MOG
parameter. We explore the energy efficiency of energy extraction and power by
applying the new energy extraction mechanism proposed by Comisso and Asenjo.
Based on an attractive gravitational charge of the MOG parameter $\alpha$ that
physically manifests to strengthen black hole gravity, we show that the
combined effect of the MOG parameter and black hole charge can play an
increasingly important role and accordingly lead to high energy efficiency and
power for the energy extraction via the magnetic reconnection. Further, we
study to estimate the rate of energy extraction under the fast magnetic
reconnection by comparing the power of the magnetic reconnection and
Blandford-Znajek (BZ) mechanisms. We show that the rate of energy extraction
increases as a consequence of the combined effect of black hole charge and MOG
parameter. It suggests that magnetic reconnection is significantly more
efficient than the BZ mechanism. In fact, the magnetic reconnection is fueled
by magnetic field energy due to the twisting of magnetic field lines around the
black hole for the plasma acceleration, and thus the MOG parameter gives rise
to even more fast spin that can strongly change the magnetic field
reconfiguration due to the frame dragging effect. This is how energy extraction
is strongly enhanced through the magnetic reconnection, thus making the energy
extraction surprisingly more efficient for the Kerr-Newman-MOG black hole than
the Kerr black hole under the combined effect of black hole charge and MOG
parameter.
