  The emission of very-high-energy photons (VHE, E>100 GeV$) in blazars is
closely connected to the production of ultra-relativistic particles and the
role of these gamma-ray sources as cosmic particle accelerators. This work
focuses on a selection of 22 gamma-ray objects from the 2BIGB catalog of
high-synchrotron-peaked sources, which are classified as blazar candidates of
uncertain type in the 4FGL-DR2 catalog. We study these sources by means of a
re-analysis of the first 10 years of gamma-ray data taken with the Fermi Large
Area Telescope, including the attenuation by the extragalactic background
light. Their broadband spectral energy distributions are also evaluated, using
multi-wavelength archival data in the radio, optical, and X-ray bands, in terms
of one-zone synchrotron-self-Compton models, adding an external Compton
component when needed. Out of this analysis, we identify 17 new extreme
high-synchrotron-peaked (EHSP) candidates and compare their physical parameters
with those of prototypical EHSP blazars. Finally, the resulting models are used
to assess their detectability by the present and future generation of
ground-based imaging atmospheric Cherenkov telescopes. We find two VHE
candidates within the reach of the current and next generation of Cherenkov
telescopes: J0847.0-2336 and J1714.0-2029.
