  In this article, the Yukawa potential is scrutinized taking into
consideration the effects of magnetic and AB flux fields within the
non-relativistic regime using the factorization method. The energy equation and
wave function of the system are obtained in close form. We find that the
all-encompassing effects result in a strongly attractive system and
consequently there is a significant upward shift in the bound state energy of
the system. We also find that to achieve a low-energy medium for the Yukawa
potential, weak magnetic field is required, however the AB flux field can be
used as a controller. The magnetic and AB fields eliminates the degeneracy from
the spectra. From our findings, it could be concluded that to manipulate the
energy spectra of this system, the AB-flux and magnetic field will do so
greatly. The results from this study can be applied in condensed matter
physics, atomic and molecular physics.
