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We solve the Schr(o)dinger equation with a position-dependent mass (PDM) charged particle interacted via the superposition of the Morse-plus-Coulomb potentials and is under the influence of exteal magnetic and Aharonov-Bohm (AB) flux fields.The nonrelativistic bound state energies together with their wave functions are calculated for two spatially-dependent mass distribution functions.We also study the thermal quantifies 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 states as a function of various physical parameters.The behavior of the inteal 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.