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The influence of external magnetic and Aharonov‐Bohm (AB) flux fields on the energy spectra and thermal properties of N2, NO, CO and H2 diatomic molecules are investigated in this study. The two‐dimensional Schrödinger equation is solved with the Varshni‐screened Coulomb potential (VSCP) model using the well‐known Nikiforov‐Uvarov (NU) method. We obtained the energy eigenvalues and wavefunctions of the system and calculated the energy levels of some diatomic molecules in the m‐arbitrary state in the presence and absence of external magnetic and AB flux fields. The results show that combining the magnetic and AB flux fields eliminates degeneracy. We analyzed and plotted the partition function and other thermal properties in the presence of a magnetic field, an AB field, and a temperature‐dependent term. [ABSTRACT FROM AUTHOR]