  This research study is primarily focus on investigating how the topological
effects influence the eigenvalue solutions in the presence of a hot-dense
medium. To accomplish this, we employ the non-relativistic Schr\"odinger wave
equation, taking into consideration both the quantum flux field and an
interaction potential. Through this approach, we determine the energy
eigenvalues and their corresponding wave functions using the Nikiforov-Uvarov
method. Our findings indicate that when we consider both the topological
effects and the magnetic flux, $\Phi$, there is a noticeable reduction in the
binding energy within the hot-dense medium. Additionally, we analyze the role
of the baryonic potential in shaping the binding energy within the $(T, u_b)$
plane. Interestingly, it is evident that the influence of the baryonic
potential becomes more pronounced as its values decrease
