  An extended, spinless Falicov-Kimball model in the presence of perpendicular
magnetic field is investigated employing Hartree-Fock self-consistent
mean-field theory in two dimensions. In the presence of an orbital field the
hybridization-dependence of the excitonic average ${ \Delta =<{{d_i}^\dagger}
{f_i}>}$ is modified. The exciton responses in subtle different ways for
different chosen values of the magnetic flux consistent with Hofstadter's
well-known spectrum. The excitonic average is suppressed by the application of
magnetic field. We further examine the effect of Coulomb interaction and
$f$-electron hopping on the condensation of exciton for some rational values of
the applied magnetic field. The interband Coulomb interaction enhances the
$\Delta$ exponentially, while a non-zero $f$-electron hopping reduces it. A
strong commensurability effect of the magnetic flux on the behaviour of the
excitons is observed.
