The stellar metallicity gradients of disc galaxies provide information on the disc assembly, star formation processes and chemical evolution. They also might store information on dynamical processes which could affect the distribution of chemical elements in the gas-phase and the stellar components. We studied the stellar metallicity gradients of stellar discs in a cosmological simulation. We explored the dependence of the stellar metallicity gradients on stellar age and the size and mass of

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... stellar discs. We used galaxies selected from a cosmological hydrodynamical simulation performed including a physically-motivated Supernova feedback and chemical evolution. The metallicity profiles were estimated for stars with different ages. We confront our numerical findings with results from the CALIFA Survey. The simulated stellar discs are found to have metallicity profiles with slopes in global agreement with observations. Low stellar-mass galaxies tend to have a larger variety of metallicity slopes. When normalized by the half-mass radius, the stellar metallicity gradients do not show any dependence and the dispersion increases significantly, regardless of galaxy mass. Galaxies with stellar masses around 10^10M_ show steeper negative metallicity gradients. The stellar metallicity gradients correlate with the half-mass radius. However, the correlation signal is not present when they are normalized by the half-mass radius. Stellar discs with positive age gradients are detected to have negative and positive metallicity gradients, depending on the relative importance of the recent star formation activity in the central regions. The large dispersions in the metallicity gradients as a function of stellar mass could be ascribed to the effects of dynamical processes such as mergers/interactions and/or migration as well as those regulating the conversion of gas into stars. [abridged]