The Javalambre-Physics of the Accelerating Universe Astrophysical Survey (J-PAS) will observe approximately one-third of the northern sky with a set of 56 narrow-band filters using the dedicated 2.55 m Javalambre Survey Telescope (JST) at the Javalambre Astrophysical Observatory. Prior to the installation of the main camera, in order to demonstrate the scientific potential of J-PAS, two small surveys were performed with the single-CCD Pathfinder camera: miniJPAS (~1 deg2 along the Extended Groth Strip), and J-NEP (~0.3 deg2 around the JWST North Ecliptic Pole Time Domain Field), including all 56 J-PAS filters as well as u, g, r, and i. J-NEP is ~0.5-1.0 mag deeper than miniJPAS, providing photometry for 24,618 r-band-detected sources and photometric redshifts (photo-z) for the 6662 sources with r < 23. In this paper, we describe the photometry and photo-z of J-NEP and demonstrate a new method for the removal of systematic offsets in the photometry based on the median colours of galaxies, which we call `galaxy locus recalibration'. This method does not require spectroscopic observations except in a few reference pointings and, unlike previous methods, is directly applicable to the whole J-PAS survey. We use a spectroscopic sample of 787 galaxies to test the photo-z performance for J-NEP and in comparison to miniJPAS. We find that the deeper J-NEP observations result in a factor ~1.5-2 decrease in σNMAD (a robust estimate of the standard deviation of the photo-z error) and η (the outlier rate) relative to miniJPAS for r > 21.5 sources, but no improvement in brighter ones, which is probably because of systematic uncertainties. We find the same relation between σNMAD and odds in J-NEP and miniJPAS, which suggests that we will be able to predict the σNMAD of any set of J-PAS sources from their odds distribution alone, with no need for additional spectroscopy to calibrate the relation. We explore the causes of photo-z outliers and find that colour-space degeneracy at low S/N, photometry artefacts, source blending, and exotic spectra are the most important factors.