Using azimuthally symmetrized cylindrical coordinates, we consider some positiondependent mass (PDM) charged particles moving in position-dependent (PD) magnetic and Aharonov-Bohm flux fields. We focus our attention on PDM-charged particles with m ( − → r ) = g (ρ) = η f (ρ) exp (−δρ) (i.e., the PDM is only radially dependent) moving in an inverse power-law-type radial PD-magnetic fieldsUnder such settings, we consider two almost-quasi-free PDM-charged particles (i.e., no interaction potential, V ( − → r ) = 0) endowed with g (ρ) = η/ρ and g (ρ) = η/ρ 2 . Both yield exactly solvable Schrödinger equations of Coulombic nature but with different spectroscopic structures. Moreover, we consider a Yukawa-type PDM-charged particle with g (ρ) = η exp (−δρ) /ρ 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 V (ρ) = −V• exp (−δρ) /ρ−V 1 /ρ+V 2 /ρ 2 . 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 with g (ρ) = η/ρ for V• = V 1 = V 2 = 0 = δ.