  Considering the regular Bardeen black hole spacetimes, we test the
observational effects of the general relativistic solutions coupled to
non-linear electrodynamics (NED) by studying the photon motion in the effective
geometry governed by the spacetime geometry and the NED Lagrangian. We focus
our attention to the observationally important case of profiled spectral lines
generated by rings radiating in a fixed frequency and orbiting the black hole
along circular geodesics of the Bardeen spacetime. Such profiled spectral lines
are observed in active galactic nuclei and in microquasars, giving sufficient
data for the test of regular black holes. We expect that such radiating rings
could arise around the Galaxy central supermassive black hole SgrA*, and the
related profiled spectral lines could give important additional information to
those obtained by direct observations due to the Event Horizon (GRAVITY)
Telescope. We demonstrate that the profiled spectral lines of the radiating
rings predict strong signatures of the NED effects on the photon motion --
namely the frequency shift to the red edge of the spectrum, and narrowing of
the profile, by more than one order in comparison with the case of the profiles
generated purely by the spacetime geometry, for all values of the magnetic
charge and the inclination angle of the observer. The specific flux is
substantially suppressed and for extended Keplerian disks even the shape of the
profiled line is significantly modified due to the NED effect.
