Blazars and in particular the subclass of high synchrotron peaked Active Galactic Nuclei are among the main targets for the present generation of Imaging Atmospheric Cherenkov Telescopes (IACTs) and will remain of great importance for very high-energy $gamma$-ray science in the era of the Cherenkov Telescope Array (CTA). Observations by IACTs, which have relatively small fields of view ($sim$ few degrees), are limited by viewing conditions; therefore, it is important to select the most promising targets in order to increase the number of detections. The aim of this paper is to search for unclassified blazars among known $gamma$-ray sources from the Fermi Large Area Telescope (LAT) third source catalog that are likely detectable with IACTs or CTA. We use an artificial neural network algorithm and updated analysis of Fermi-LAT data. We found 80 $gamma$-ray source candidates, and for the highest-confidence candidates, we calculate their potential detectability with IACTs and CTA based on an extrapolation of their energy spectra. Follow-up observations of our source candidates could significantly increase the current TeV source population sample and could ultimately confirm the efficiency of our algorithm to select TeV sources.
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