<p>In this study, we present analytical eigensolutions of the radial Schrödinger equation for a point-like global monopole under the Hulthén–Yukawa potential in higher dimensions. By employing the asymptotic iteration method together with the Greene–Aldrich approximation to handle the centrifugal barrier, we derive closed-form expressions for both the energy and the wave function. These solutions were then applied to the diatomic molecules chromium hydride and nickel carbide to analyse energy eigenvalues, wave functions, probability densities, and expectation values. The findings demonstrate a pronounced sensitivity of energy levels and expectation values to quantum states, topological defect parameters, and dimensionality. Moreover, the amplitudes of the wave functions and the probability densities increase with higher quantum states, larger dimension number, and lower topological defect parameters, offering key insights into the influence of topological defects on molecular behavior in higher-dimensional spaces.</p>