  We test the anisotropy in the Finslerian cosmological model with the X-ray
and ultraviolet (UV) fluxes of 808 quasars. The dipole amplitude is
$A_D=0.302_{ -0.124}^{ +0.185}$ and the dipole direction points towards $(l, b)
= ( 288.92_{~ -28.80^{\circ}}^{^{\circ}+23.74^{\circ}}, 6.10_{~
-16.40^{\circ}}^{^{\circ} +16.55^{\circ}} )$. We find that the dipole direction
from the X-ray and UV fluxes of quasars is very close to the dipole direction
given by the "Joint Light-curve Analysis" (JLA) compilation in the Finslerian
cosmological model and the angular difference between the two dipole directions
is only $10.44^{\circ}$. We also find the angular difference between the dipole
direction from the 808 quasars in the Finslerian cosmological model and ones
from the supernovae of type Ia (SNe Ia) samples in the dipole-modulated
$\Lambda$CDM model is around $30^{\circ}$. Six gravitationally lensed quasars
are considered to investigate the Hubble constant $H_0$ in the Finslerian
cosmological model. We get a slightly smaller $H_0$ than the result given by
the six gravitationally lensed quasars. Finally, we forecast the future
constraints on the dipole parameters with the X-ray and UV fluxes of quasars.
As the number of simulations increases, the precisions of the parameters
related to anisotropy in the Finslerian cosmological model improve
significantly. The X-ray and UV fluxes of quasars have a promising future as a
probe of anisotropy in Finsler spacetime.
