  This paper studied the relativistic accretion thick disc model raised by a
deformed compact object that slightly deviated from spherical up to the
quadrupole moment by utilising $\rm q$-metric. This metric is the simplest
asymptotically flat solution of Einstein's equation with quadrupole moment.
This work aims to study the effects of quadrupole moments in combination with
the parameters of the thick magnetised disc model via studying the properties
of these equilibrium sequences of magnetised, non-self-gravitating discs in
this space-time. We employed different angular momentum distributions and
discussed the procedure of building this toroidal disc model based on a
combination of approaches previously considered in the literature. We have
shown the properties of this relativistic accretion disc model and its
dependence on the initial parameters. Besides, this theoretical model can be
served as the initial data for numerical simulations.
