  The Israel-Carter theorem (also known as the ``no-hair theorem'') puts a
restriction on the existence of parameters other than mass, electric charge,
and angular momentum of a black hole. In this context, Bekenstein proposed
no-hair theorems in various black hole models with neutral and electrically
charged scalar fields.
  In this paper, we take the Einstein-Maxwell-charged scalar model with an
electrically charged scalar field gauge-coupled to the Maxwell field
surrounding a charged black hole in the background of a static spherically
symmetric metric. We ascertain the validity of all energy conditions coupled
with the causality condition, suggesting the possibility of existence of
charged hairy solutions. Consequently, we obtain, by exact numerical
integration, detailed solutions of the field equations in this model. The
solutions exhibit damped oscillatory behaviours for the charged scalar hair. We
also find that the electric potential $V(r)$ is a monotonic function of $r$, as
required by electrodynamics.
  Furthermore, we find that the charged hairy solutions are stable against
time-dependant perturbations about the static solutions. We ascertain their
stability by carrying out dynamic stability analyses, employing two different
methodologies. The first methodology is based on a Sturm-Liouville equation,
whereas the second methodology employs a Schr\"odinger-like equation for the
dynamic perturbations. We find stability of the charged hairy solutions in both
stability analyses.
