  In this work, we investigate the behavior of non-relativistic quantum
particles immersed in a cosmic string space-time background. Our study involves
the examination of these particles as they interact with a range of influences,
including potential, magnetic, and quantum flux fields. We employ analytical
methods to solve the associated wave equation, leading to the derivation of
eigenvalue solutions for this quantum system. Subsequently, we leverage these
eigenvalue solutions to scrutinize several potential models. For each model, we
present and engage in a thorough discussion of the corresponding eigenvalue
solutions. In an extension of our investigation, we explore the thermodynamic
and magnetic properties of the quantum system when it is exposed to non-zero
temperature conditions, denoted by $T \neq 0$. Our analysis encompasses the
calculation of essential parameters such as the partition function for the
system and other pertinent functions. Following these calculations, we
meticulously examine and interpret the outcomes, shedding light on the system's
behavior and characteristics in the presence of temperature variations.
Furthermore, we calculate entropic information to investigate the location of
particles in the system.
