  Context. The recent discovery of several ultra high-energy gamma-ray emitters
in our Galaxy represents a significant advancement towards the characterisation
of its most powerful accelerators. Nonetheless, in order to unambiguously
locate the regions where the highest energy particles are produced and
understand the responsible physical mechanisms, detailed spectral and
morphological studies are required, especially given that most of the observed
sources were found to be significantly extended. Aims. In these regards,
pointing observations with the next-generation Imaging Atmospheric Cherenkov
Telescopes, such as the Cherenkov Telescope Array (CTA) Observatory and the
ASTRI Mini-Array (ASTRI), are expected to provide significant improvements.
Here we aim to identify the most promising sources to target in future
observations. Methods. For this purpose, we performed a comparative analysis of
the expected performance of ASTRI and CTA, computing their differential
sensitivities towards extended sources, and further explored their capabilities
with respect to specific case studies, including follow-ups of existing
gamma-ray source catalogues. Results. We find that almost all of the sources
thus far detected by LHAASO-WCDA and in the H.E.S.S. Galactic Plane Survey will
be in the reach of ASTRI and CTA with about 300 and 50 hours of exposure,
respectively. For the highest energy emitters detected by LHAASO-KM2A, in turn,
we provide a list of the most promising objects that would require further
investigation. We additionally examined specific classes of sources in order to
identify potentially detectable gamma-ray emitters, such as passive molecular
clouds (i.e. illuminated by the cosmic-ray sea) and pulsars surrounded by a
halo of runaway particles.
