  The aim of this work is to improve models for the gamma-ray discrete or
small-scale structure related to H2 interstellar gas. Reliably identifying this
contribution is important to disentangle gamma-ray point sources from
interstellar gas, and to better characterize extended gamma-ray signals.
Notably, the Fermi-LAT Galactic center (GC) excess, whose origin remains
unclear, might be smooth or point-like. If the data contain a point-like
contribution that is not adequately modeled, a smooth GC excess might be
erroneously deemed to be point-like. We improve models for the H2-related
gamma-ray discrete emission for a $50^\circ \times 1^\circ$ region along the
Galactic plane via H2 proxies better suited to trace these features. We find
that these are likely to contribute significantly to the gamma-ray Fermi-LAT
data in this region, and the brightest ones are likely associated with detected
Fermi-LAT sources, a compelling validation of this methodology. We discuss
prospects to extend this methodology to other regions of the sky and
implications for the characterization of the GC excess.

High Energy Astrophysical Phenomena;Astrophysics of Galaxies;High Energy Physics - Phenomenology