<p>In this study, we investigate the energy spectrum and thermodynamic properties of a quantum system subjected to the Varshni-Hellmann potential in the presence of an external magnetic field and an Aharonov–Bohm (AB) flux field. By employing the Nikiforov–Uvarov Functional Analysis (NUFA) method, we obtain the exact analytical solutions for the Schrödinger equation, leading to explicit expressions for the energy eigenvalues and corresponding wavefunctions. The combined influence of the potential parameters, magnetic field strength, and AB flux on the energy spectrum is analyzed in detail. Furthermore, we explore the statistical mechanics of the system by deriving the partition function using the obtained energy spectrum. Various thermodynamic quantities such as the Helmholtz free energy, mean energy, entropy, and heat capacity are computed and discussed in the context of their dependence on the system parameters. Our findings provide valuable insights into quantum systems with mixed potentials and external fields, with potential applications in condensed matter physics and quantum information science.</p>