  Axion-like particles (ALPs), predicted in theories beyond the Standard Model,
can have observational effects on the transparency of the Universe to $\gamma$
rays in the presence of magnetic fields. In this work, we search for effects
compatible with the existence of ALPs with 80 months of data from the ${\it
Fermi}$ Large Area Telescope, by comparing the distributions of observed
highest energy photons from sources beyond redshifts of z $\geq$ 0.1 with
theoretical predictions in the presence of ALPs. We find no evidence for an
increased $\gamma$-ray transparency due to ALPs and therefore we set limits on
the ALPs parameters assuming a value of the intergalactic magnetic field
strength of 1 nG. Photon-ALP couplings above $10^{-11}$ GeV$^{-1}$ are excluded
for ALP masses $m_{a}$ $\lesssim3.0$ neV. These limits exclude a region of the
parameter space not covered by other $\gamma$-ray telescopes and are compatible
with constraints imposed by other experiments.
