  The anomalous decay rate of the quasinormal modes occurs when the
longest-lived modes are the ones with higher angular number. Such behaviour has
been recently studied in different static spacetimes, for uncharged scalar and
fermionic perturbations, being observed in both cases. In this work we consider
the propagation of charged massive scalar fields in the background of
Reissner-Nordstr\"om-de Sitter black holes and we mainly study the effect of
the scalar field charge in the spectrum of quasinormal frequencies, as well as,
its effect on the anomalous decay rate. Mainly, we show that the anomalous
behaviour is present for massive charged scalar fields as well, and a critical
value of scalar field mass exists, beyond which the behaviour is inverted.
However, there is also a critical value of the parameter $qQ$ of the charge of
the scalar field and of the charge of the black hole, which increases when the
cosmological constant increases, and beyond the critical value the anomalous
behaviour of the decay rate could be avoided for the fundamental mode.
