  We study the properties of a hot and magnetized quark matter in a rotating
cylinder in the presence of a constant magnetic field. To do this, we solve the
corresponding Dirac equation using the Ritus eigenfunction method. This leads
to the energy dispersion relation, Ritus eigenfunctions, and the quantization
relation for magnetized fermions. To avoid causality-violating effects, we
impose a certain global boundary condition, and study its effect, in
particular, on the energy eigenmodes and the quantization relations of
fermions. Using the fermion propagator arising from this method, we then solve
the gap equation at zero and nonzero temperatures. At zero temperature, the
dynamical mass $\bar{m}$ does not depend on the angular frequency, as expected.
We thus study its dependence on the distance $r$ relative to the axis of
rotation and the magnetic field $B$, and explore the corresponding finite size
effect for various couplings $G$. We then consider the finite temperature case.
The dependence of $\bar{m}$ on the temperature $T$, magnetic field $B$, angular
frequency $\Omega$, and distance $r$ for various $G$ is studied. We show that
$\bar{m}$ decreases, in general, with $B$ and $\Omega$. This is the ''inverse
magneto-rotational catalysis (IMRC)'' or the ''rotational magnetic
inhibition'', previously discussed in the literature. To explore the evidence
of this effect in the phase diagrams of our model, we examine the phase
portraits of the critical temperature $T_c$ as well as the critical angular
frequency $\Omega_c$ with respect to $G, B,\Omega$, and $r$ as well as $G, B,
T$, and $r$, respectively. We show that $T_{c}$ and $\Omega_c$ decrease, in
particular, with $B$. This is interpreted as clear evidence for IMRC.
