  The metallicity gradients of the stellar populations in disc galaxies and
their evolution store relevant information on the disc formation history and on
those processes which could mix stars a posteriori, such as migration, bars
and/or galaxy-galaxy interactions. We aim to investigate the evolution of the
metallicity gradients of the whole stellar populations in disc components of
simulated galaxies in a cosmological context. We analyse simulated disc
galaxies selected from a cosmological hydrodynamical simulation that includes
chemical evolution and a physically motivated Supernova feedback capable of
driving mass-loaded galactic winds. We detect a mild evolution with redshift in
the metallicity slopes of $-0.02 \pm 0.01$ dex~kpc$^{-1}$ from $z\sim 1$. If
the metallicity profiles are normalised by the effective radius of the stellar
disc, the slopes show no clear evolution for $z < 1$, with a median value of
approximately $-0.23$ dex ~$r_{\rm reff}^{-1}$. As a function of stellar mass,
we find that metallicity gradients steepen for stellar masses smaller than
$\sim 10^{10.3} {\rm M_{\odot}}$ while the trend reverses for higher stellar
masses, in the redshift range $z=[0,1]$. Galaxies with small stellar masses
have discs with larger $r_{\rm reff}$ and flatter metallicity gradients than
expected. We detect migration albeit weaker than in previous works. Our stellar
discs show a mild evolution of the stellar metallicity slopes up to $z\sim 1,$
which is well-matched by the evolution calculated archeologically from the
abundance distributions of mono-age stellar populations at $z\sim 0$. Overall,
Supernova feedback could explain the trends but an impact of migration can not
be totally discarded. Galaxy-galaxy interactions or small satellite accretions
can also contribute to modify the metallicity profiles in the outer parts.
[abridged]
