  We conduct a theoretical study of the creation and dynamics of vortices in a
two-dimensional binary Bose-Einstein condensate with a mass imbalance between
the species. To initiate the dynamics, we use one or two rotating paddle
potentials in one species, while the other species is influenced only via the
interspecies interaction. In both species, the number and the dominant sign of
the vortices are determined by the rotation frequency of the paddle potential.
Clusters of positive and negative vortices form at a low rotation frequency
comparable to that of the trap when using the single paddle potential. In
contrast, vortices of the same sign tend to dominate as the rotation frequency
of the paddle increases, and the angular momentum reaches a maximum value at a
paddle frequency, where the paddle velocity becomes equal to the sound velocity
of the condensate. When the rotation frequency is sufficiently high, the rapid
annihilation of vortex-antivortex pairs significantly reduces the number of
vortices and antivortices in the system. For two paddle potentials rotating in
the same direction, the vortex dynamics phenomenon is similar to that of a
single paddle. However, when the paddle potentials are rotated in the opposite
direction, both positive and negative signed vortices occur at all rotational
frequencies. At the low rotation frequencies, the cluster of like-signed
vortices produces the $k^{-5/3}$ and $k^{-3}$ power laws in the incompressible
kinetic energy spectrum at low and high wavenumbers, respectively, a hallmark
of the quantum turbulent flows.
