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Narrow-line Seyfert 1 galaxies (NLSy1s) are a well-established class of$\gamma$-ray sources, showing the presence of a jet like the more commonflat-spectrum radio quasars. The evidence of $\gamma$-ray emission poses theissue of the location of the $\gamma$-ray emitting zone and of the contributionof the $\gamma$-$\gamma$ absorption within the broad-line region (BLR), sincesuch objects have been detected by Fermi-LAT in the MeV-GeV energy range butnot by imaging atmospheric Cherenkov telescopes beyond 100 GeV. We discuss howthe spectral properties of three NLSy1s (SBS 0846+513, PMN J0948+0022, and PKS1502+036) derived from the Fermi Large Area Telescope Fourth Source Catalog(4FGL) compare with theoretical models based on the observed properties of theBLR. In particular, we focus on the question on how simple power-law spectralmodels and log-parabolic ones could be disentangled in $\gamma$-ray narrow-lineSeyfert 1 galaxies by means of current Fermi-LAT or future imaging atmosphericCherenkov telescopes data. We find that the only possibility for alog-parabolic model to mimic a power-law model in the energy band above $E \sim100$ GeV is to have a very small value of the curvature parameter $ \beta \sim0.05$.

High-energy and Very High-energy Constraints from Log-parabolic Spectral Models in Narrow-line Seyfert 1 Galaxies