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Full coverage of the 3800\u20139100 \u00c5 range with 54 narrow-band filters, in combination with 6 optical broad-band filters, allows for extremely accurate photometric redshifts (photo-<jats:italic>z<\/jats:italic>), which, applied over areas of thousands of square degrees, will enable new applications of the photo-<jats:italic>z<\/jats:italic> technique, such as measurement of baryonic acoustic oscillations. In this paper we describe the method we used to obtain the photo-<jats:italic>z<\/jats:italic> that is included in the publicly available miniJPAS catalogue, and characterise the photo-<jats:italic>z<\/jats:italic> performance. We built photo-spectra with 100 \u00c5 resolution based on forced-aperture photometry corrected for point spread function. Systematic offsets in the photometry were corrected by applying magnitude shifts obtained through iterative fitting with stellar population synthesis models. We computed photo-<jats:italic>z<\/jats:italic> with a customised version of L<jats:sc>E<\/jats:sc>P<jats:sc>HARE<\/jats:sc>, using a set of templates that is optimised for the J-PAS filter-set. We analysed the accuracy of miniJPAS photo-<jats:italic>z<\/jats:italic> and their dependence on multiple quantities using a subsample of 5266 galaxies with spectroscopic redshifts from SDSS and DEEP, which we find to be representative of the whole <jats:italic>r<\/jats:italic> &lt; 23 miniJPAS sample. Formal 1<jats:italic>\u03c3<\/jats:italic> uncertainties for the photo-<jats:italic>z<\/jats:italic> that are calculated with the \u0394<jats:italic>\u03c7<\/jats:italic><jats:sup>2<\/jats:sup> method underestimate the actual redshift errors. The <jats:italic>o<\/jats:italic><jats:italic>d<\/jats:italic><jats:italic>d<\/jats:italic><jats:italic>s<\/jats:italic> parameter has a stronger correlation with |\u0394<jats:italic>z<\/jats:italic>| and accurately reproduces the probability of a redshift outlier (|\u0394<jats:italic>z<\/jats:italic>| &gt; 0.03), regardless of the magnitude, redshift, or spectral type of the sources. We show that the two main summary statistics characterising the photo-<jats:italic>z<\/jats:italic> accuracy for a population of galaxies (<jats:italic>\u03c3<\/jats:italic><jats:sub>NMAD<\/jats:sub> and <jats:italic>\u03b7<\/jats:italic>) can be predicted by the distribution of <jats:italic>o<\/jats:italic><jats:italic>d<\/jats:italic><jats:italic>d<\/jats:italic><jats:italic>s<\/jats:italic> in this population, and we use this to estimate the statistics for the whole miniJPAS sample. At <jats:italic>r<\/jats:italic> &lt; 23, there are \u223c17 500 galaxies per deg<jats:sup>2<\/jats:sup> with valid photo-<jats:italic>z<\/jats:italic> estimates, \u223c4200 of which are expected to have |\u0394<jats:italic>z<\/jats:italic>| &lt; 0.003. The typical error is <jats:italic>\u03c3<\/jats:italic><jats:sub>NMAD<\/jats:sub> = 0.013 with an outlier rate <jats:italic>\u03b7<\/jats:italic> = 0.39. 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