I. Sample and methods

[Context]: The controversy about the origin of the structure of early-type S0-E/S0 galaxies may be due to the difficulty of comparing surface brightness profiles with different depths, photometric corrections and point spread function (PSF) effects (which are almost always ignored). [Aims]: We aim to quantify the properties of Type-III (anti-truncated) discs in a sample of S0 galaxies at 0.2 <z< 0.6. In this paper, we present the sample selection and describe in detail the methods to robustly trace the structure in their outskirts and correct for PSF effects. [Methods]: We have selected and classified a sample of 150 quiescent galaxies at 0.2 <z< 0.6 in the GOODS-N field. We performed a quantitative structural analysis of 44 S0-E/S0 galaxies. We have corrected their surface brightness profiles for PSF distortions and analysed the biases in the structural and photometric parameters when the PSF correction is not applied. Additionally, we have developed Elbow, an automatic statistical method to determine whether a possible break is significant-or not-and its type. We have made this method publicly available. [Results]: We find 14 anti-truncated S0-E/S0 galaxies in the range 0.2 <z< 0.6 (~30% of the final sample). This fraction is similar to the those reported in the local Universe. In our sample, ~25% of the Type-III breaks observed in PSF-uncorrected profiles are artifacts, and their profiles turn into a Type I after PSF correction. PSF effects also soften Type-II profiles. We find that the profiles of Type-I S0 and E/S0 galaxies of our sample are compatible with the inner profiles of the Type-III, in contrast with the outer profiles. [Conclusions]: We have obtained the first robust and reliable sample of 14 anti-truncated S0-E/S0 galaxies beyond the local Universe, in the range 0.2 <z< 0.6. PSF effects significantly affect the shape of the surface brightness profiles in galaxy discs even in the case of the narrow PSF of HST/ACS images, so future studies on the subject should make an effort to correct them.Supported by the Ministerio de Economía y Competitividad del Gobierno de España (MINECO) under project AYA2012-31277 and project P3/86 of the Instituto de Astrofisica de Canarias. PGP-G acknowledges support from MINECO grants AYA2015-70815-ERC and AYA2015-63650-P.Peer Reviewe