  High energy gamma-rays propagating in external magnetic fields may convert
into axion-like particles (ALPs). In this case, the observed gamma-ray spectra
are modified by the resulting energy-dependent conversion probability. In this
study, we use the energy spectra of 20 extra-galactic gamma-ray sources
recorded during 10 years of \textit{Fermi}-LAT observations. We define a test
statistics based upon the likelihood ratio to test the hypothesis for a
spectral model without vs. a model with photon-ALPs coupling. The conversion
probability is calculated for fixed values of the mass and two-photon coupling
of the pseudo-scalar particle while the external magnetic field is
characterized by the additional free parameters length scale $s$ and average
field strength $B$. As a consistency check and in order to extend the analysis
to include very high energy gamma-ray data, another test statistics is defined
with the $\chi^2$ method. We find for 18 of the 20 sources a favorable fit,
particularly for Markarian~421 and NGC~1275 a significant improvement, with the
hypothesis of photon-ALPs coupling in likelihood analysis. The test statistics
of the sources are combined and the significance has been estimated
$5.3~\sigma$ (test statistics summed in local maxima of all sources) and
$6.0~\sigma$ (global maxima). The significance is estimated from dedicated
simulations under the null hypotheses. The locally best-fitting values of $B$
and $s$ fall into the range that is expected for large scale magnetic fields
present in relevant astrophysical environments.
