  Using azimuthally symmetrized cylindrical coordinates, we consider some
position-dependent mass (PDM) charged particles moving in position-dependent
(PD) magnetic and Aharonov-Bohm flux fields. We focus our attention on
PDM-charged particles (i.e., the PDM is only radially dependent) moving in an
inverse power-law-type radial PD-magnetic fields. Under such settings, we
consider two almost-quasi-free PDM-charged particles (i.e., no interaction
potential). Both yield exactly solvable Schr\"odinger equations of Coulombic
nature but with different spectroscopic structures. Moreover, we consider a
Yukawa-type PDM-charged particle moving not only in the vicinity of the
PD-magnetic and Aharonov-Bohm flux fields but also in the vicinity of a Yukawa
plus a Kratzer type potential force field. For this particular case, we use the
Nikiforov-Uvarov (NU) method to come out with exact analytical eigenvalues and
eigenfunctions. Which, in turn, recover those of the almost-quasi-free
PDM-charged particle. Energy levels crossings are also reported.
