Gamma-ray emitting narrow-line Seyfert 1 ($\gamma$-NLSy1) galaxies are jetted sources hosting a relatively low-mass black hole (10$^6$--10$^8$ $M_{\odot}$) which accretes close to the Eddington limit. $\gamma$-NLSy1 galaxies show flux and spectral variability in the gamma-ray energy band and radio properties similar to those of blazars, which indicate the presence of a relativistic jet. These properties make them interesting to investigate with the Cherenkov Telescope Array (CTA), the next-generation ground-based gamma-ray observatory.
CTA will cover the 20 GeV--300 TeV energy range, with an improvement in average differential sensitivity by a factor 5--20 with respect to the current imaging atmospheric Cherenkov telescope arrays. For transients/flaring events (timescales of $\sim 1$ day or shorter) CTA will be about two orders of magnitude more sensitive with respect to Fermi-LAT at the overlapping energy of 25 GeV, allowing an unprecedented opportunity to investigate flaring $\gamma$-NLSy1 galaxies. We present preliminary results obtained by simulating the prototypical $\gamma$-NLSy1 galaxy, PMN~J0948$+$0022, by means of the CTA public {\tt ctools} software and the public instrument response files,
investigating its possible detection and spectral properties, taking into account the effect of both the extra-galactic background light and intrinsic absorption components.