Well-motivated extensions of the standard model predict ultra-light and fundamental pseudo-scalar particles (e.g., axions or axion-like particles: ALPs). Similarly to the Primakoff-effect for axions, ALPs can mix with photons and consequently be searched for in laboratory experiments and with astrophysical observations. Here, we search for energy-dependent modulations of high-energy gamma-ray spectra that are tell-tale signatures of photon-ALPs mixing. To this end, we analyze the data recorded with the Fermi-LAT from Galactic pulsars selected to have a line of sight crossing spiral arms at a large pitch angle. The large-scale Galactic magnetic field traces the shape of spiral arms, such that a sizable photon-ALP conversion probability is expected for the sources considered. For the nearby Vela pulsar, the energy spectrum is well described by a smooth model spectrum (a power-law with a sub-exponential cut-off) while for the six selected Galactic pulsars, a common fit of the ALPs parameters improves the goodness of fit in comparison to a smooth model spectrum with a significance of 4.6 σ. We determine the most-likely values for mass ma and coupling gaγγ to be ma=(3.6−0.2 stat.+0.5 stat.± 0.2syst. ) neV and gaγγ=(2.3−0.4stat.+0.3 stat.± 0.4syst.)× 10−10 GeV−1. In the error budget, we consider instrumental effects, scaling of the adopted Galactic magnetic field model (± 20 %), and uncertainties on the distance of individual sources. The best-fit parameters are by a factor of ≈ 3 larger than the current best limit on solar ALPs generation obtained with the CAST helioscope, although known modifications of the photon-ALP mixing in the high density solar environment could provide a plausible explanation for the apparent tension between the helioscope bound and the indication for photon-ALPs mixing reported here.