  We consider the propagation of a charged massive scalar field in the
background of a four-dimensional Ernst black hole and study its stability
analyzing the quasinormal modes (QNMs), which are calculated using the
semi-analytical Wentzel-Kramers-Brillouin method and numerically using the
continued fraction method. Mainly, we find that for a scalar field mass less
than a critical mass, the decay rate of the QNMs decreases when the harmonic
angular number $\ell$ increases; and for a scalar field mass greater than the
critical mass the behaviour is inverted, i.e, the longest-lived modes are
always the ones with the lowest angular number recovering the standard
behaviour. Also, we find a critical value of the external magnetic field, as
well as, a critical value of the scalar field charge that exhibit the same
behaviour with respect to the angular harmonic numbers. In addition, we show
that the spacetime allows stable quasibound states and we observe a splitting
of the spectrum due to the Zeeman effect. Finally, we show that the unstable
null geodesic in the equatorial plane is connected with the QNMs when the
azimuthal quantum number satisfy $m= \pm \ell$ in the eikonal limit.
