  We study the instability of near extremal and extremal four-dimensional AdS
charged hairy black hole to radial neutral massive and charged massless scalar
field perturbations. We solve the scalar field equation by using the improved
asymptotic iteration method and the time domain analysis and we find the
quasinormal frequencies. For the charged scalar perturbations, we find the
superradiance condition by computing the reflection coefficient in the
low-frequency limit and we show that in the superradiance regime, which depends
on the scalar hair charge, all modes of radial charged massless perturbations
are unstable, indicating that the charged hairy black hole is superradiantly
unstable. On the other hand, calculating the quasinormal frequencies of radial
neutral scalar perturbations in this background, we found stability of the
charged hairy black hole.
