  Astrophysical sources of very high energy (VHE; $>100$ GeV) $\gamma$ rays are
rare, since GeV and TeV photons can be only emitted in extreme circumstances
involving interactions of relativistic particles with local radiation and
magnetic fields. In the context of the Fermi Large Area Telescope (LAT), only a
few sources are known to be VHE emitters, where the largest fraction belongs to
the rarest class of active galactic nuclei: the blazars. In this work, we
explore Fermi-LAT data for energies $>100$ GeV and Galactic latitudes $b >
|50^{\circ}|$ in order to probe the origin of the extragalactic isotropic
$\gamma$-ray emission. Since the production of such VHE photons requires very
specific astrophysical conditions, we would expect that the majority of the VHE
photons from the isotropic $\gamma$-ray emission originate from blazars or
other extreme objects like star-forming galaxies, $\gamma$-ray bursts, and
radio galaxies, and that the detection of a single VHE photon at the adopted
Galactic latitudes would be enough to unambiguously trace the presence of such
a counterpart. Our results suggest that blazars are, by far, the dominant class
of source above 100 GeV, although they account for only $22.8^{+4.5}_{-4.1}\%$
of the extragalactic VHE photons. The remaining $77^{+4.1}_{-4.5}\%$ of the VHE
photons still have an unknown origin.

High Energy Astrophysical Phenomena