XXL-HSC: An updated catalogue of high-redshift ($z\geqslant3.5$) X-ray
  AGN in the XMM-XXL northern field. Constraints on the bright end of the soft
  logN-logS
  X-rays offer a reliable method to identify Active Galactic Nuclei (AGN).
However, in the high-redshift Universe X-ray AGN are poorly sampled due to
their relatively low space density and the small areas covered by X-ray
surveys. In addition to wide-area X-ray surveys, it is important to have deep
optical data in order to locate the optical counterparts and determine their
redshifts. In this work, we build a high-redshift ($z\geqslant3.5$) X-ray
selected AGN sample in the XMM-XXL northern field using the most updated [0.5-2
keV] catalogue along with a plethora of new spectroscopic and multi-wavelength
catalogues, including the deep optical Subaru Hyper Suprime-Cam (HSC) data
reaching magnitude limits i$\sim$26 mag. We select all the spectroscopically
confirmed AGN and complement this sample with high-redshift candidates that are
HSC g- and r-band dropouts. To confirm the dropouts, we derive their
photometric redshifts using spectral energy distribution techniques. We end up
with a sample of 54 high-z sources (28 with spec-z), the largest in this field
so far (almost three times larger than in previous studies), and we estimate
the possible contamination and completeness. We calculate the number counts
(logN-logS) in different redshift bins and compare our results with previous
studies and models. We provide the strongest high-redshift AGN constraints yet
at bright fluxes ($\rm f_{0.5-2~keV} > 10^{-15} erg~s^{-1}~cm^{-2}$). The
samples of $z\geqslant3.5$, $z\geqslant4$ and $z\geqslant5$ are in agreement
with an exponential decline model similar to that witnessed at optical
wavelengths. Our work emphasizes the importance of using wide area X-ray
surveys with deep optical data to uncover high redshift AGN.
