  We study the phenomena of superradiance for $F(R)$-Maxwell black holes in an
AdS space-time. The AdS boundary plays the role of a mirror and provides a
natural confining system that makes the superradiant waves bouncing back and
forth between the region near the horizon and the reflective boundary, causing
a possible superradiant instability. We obtain numerical solutions for static
hairy black holes in this scenario and investigate their instability and
explicitly address the stability of such solutions for spherical perturbations
under specific conditions for the scalar charge and AdS radius. It is shown
that for a small scalar charge or AdS radius the static hairy solution is
stable under spherical perturbations. We conclude that under such conditions,
new hairy black holes emerge as a possible endpoint of superradiant instability
of the system.
