The High Altitude Water Cherenkov (HAWC) Observatory is a wide-field-of-view gamma-ray observatory that is optimized to detect gamma rays between ~300 GeV and several hundred TeV. The HAWC Collaboration recently released their third source catalog (3HWC), which contains 65 sources. One of these sources, the ultra-high-energy gamma-ray source 3HWC J1908+063, may exhibit a hardening of the spectral index at the highest energies (above 56 TeV). At least two populations of particles are needed to satisfactorily explain the highest energy emission. This second component could be leptonic or hadronic in origin. If it is hadronic in origin, it would imply the presence of protons with energies up to $sim$1 PeV near the source. We have searched other 3HWC sources for the presence of this spectral hardening feature. If observed, this would imply that the sources could make good PeVatron candidates.
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