  The amplitude of the metagalactic ultraviolet background (UVB) at
large-scales is impacted by two factors. First, it naturally attenuates at
scales larger than mean-free-path of UVB photons due to the absorption by
neutral intergalactic medium. Second, there are discrete and rare ionizing
sources distributing in the Universe, emitting the UVB photons, and thus
enhancing the local UVB amplitude. Therefore, for cosmological probe that is
sensitive to the UVB amplitude and capable of detecting the large scale like
Lyman-$\alpha$ forest spectrum, the fluctuation due to the clustering of
ionizing sources becomes a significant factor for Lyman-$\alpha$ flux
transmission and leave imprints on Lyman-$\alpha$ flux power spectrum at these
large scales. In this work, we make use of a radiative transfer model that
parametrizes the UVB source distribution by its bias $b_{\rm j}$ and shot noise
$\overline{n}_{\rm j}$. We estimate the constraints on this model through the
cross-correlation between Lyman-$\alpha$ forest survey and galaxy survey, using
the DESI Lyman-$\alpha$ forest survey and the Roman Space Telescope emission
line galaxy survey as an example. We show the detection sensitivity improvement
for UVB parameters from disjoint to maximal overlap of DESI+Roman survey
strategy. We also show that the degeneracy of two ionizing source parameters
can be broken by increasing the overlapping survey area. Our results motivate
survey strategies more dedicated to probe the UVB large-scale fluctuations.
