  In this paper, we study the quasinormal mode and late-time tail of charged
massless scalar perturbations of a black hole in the generalized Rastall
gravity. The black hole metric in question is spherically symmetric,
accompanied by a power-Maxwell field surrounded by a quintessence fluid. It is
shown that the massless scalar field, when {\it dressed up} with the magnetic
field, acquires an effective mass which, in turn, significantly affects the
properties of the resultant quasinormal oscillations and late-time tails. To be
specific, the quasinormal frequencies become distorted and might even be
unstable for particular spacetime configurations. Also, the exponent of the
usual power-law tail is modified in accordance with the modification in the
structure of the branch cut of the retarded Green's function. In particular, as
the effective mass is generated dynamically due to the presence of the magnetic
field, one may consider a process through which the field is gradually removed
from the spacetime configuration. In this context, while the quasinormal
oscillations converge to the case of massless perturbations, we argue that the
properties of resultant late-time tails do not fall back to their massless
counterpart. The relevant features are investigated by numerical and analytic
approaches.
