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In this work, the thermodynamic properties of pseudo-harmonic potential in the presence of external magnetic and Aharanov-Bohm fields are investigated. The effective Boltzmann factor in the superstatistics formalism was used to obtain the thermodynamic properties such as Helmholtz free energy, Internal energy, entropy and specific heat capacity of the system. In addition, the thermal properties of some selected diatomic molecules of N2,Cl2,I2 and CH using their experimental spectroscopic parameters and the effect of varying the deformation parameter of q=0,0.3,0.7 were duly examined.