  We solve the Schr\"odinger equation with a position-dependent mass (PDM)
charged particle interacted via the superposition of the Morse and Coulomb
potentials and exposed to external magnetic and Aharonov-Bohm (AB) flux fields.
The non-relativistic bound state energies together with their wave functions
are calculated for two spatially-dependent mass distribution functions. We also
study the thermal quantities of such a system. Further, the canonical formalism
is used to compute various thermodynamic variables for second choosing mass by
using the Gibbs formalism. We give plots for energy as a function of various
physical parameters. The behavior of the internal energy, specific heat and
entropy as functions of temperature and mass density parameter in the
inverse-square mass case for different values of magnetic field are shown.
