  We investigate the combined finite-size and thermo-magnetic effects on the
properties of the quark matter, in the context of the two-flavored
Nambu--Jona-Lasinio model. In particular, by using the mean-field approximation
and the Schwinger proper time method in a toroidal topology with periodic or
antiperiodic conditions, we evaluate the chiral phase transition, the
constituent quark mass and the thermal and spatial susceptibilities under the
change of the size, temperature and strength of external magnetic field. To
take into account the inverse magnetic catalysis phenomenon, we make use of a
recently proposed magnetized coupling constant. The findings suggest that the
observables are strongly affected by the variation of the variables and also by
the periodicity of the boundary conditions, with the final outcomes depending
on the balance of these competing phenomena.
