  The emission of very-high-energy photons (VHE, E$>$100 GeV) in active
galactic nuclei (AGN) is closely connected with the production of
ultra-relativistic particles. Among AGN, the subclass of extreme BL Lacertae
are of particular interest because they challenge state-of-art models on how
these cosmic particle accelerators operate. By cross-matching two gamma-ray
catalogs (this is, 4FGL-DR2 and 2BIGB), we identified 23
high-synchrotron-peaked (HSP) blazar candidates with photometric or
spectroscopic redshifts, good multi-wavelength coverage, that are possibly
detectable by VHE instruments. We performed a new analysis of Fermi Large Area
Telescope data including the effects of attenuation from the extragalactic
background light and complemented these results by collecting multiwavelength
data from optical, radio and X-ray archival observations. Their broadband
spectral energy distributions were interpreted in terms of
synchrotron-self-Compton models with external-Compton components and compared
with the properties of prototypical extreme HSP blazars. Finally, we test their
detectability with imaging atmospheric Cherenkov telescopes (IACTs) and propose
a new method for selecting these extreme targets for these ground-based
telescopes.
