  We describe the Dark Energy Survey (DES) Deep Fields, a set of images and
associated multi-wavelength catalogue ($ugrizJHKs$) built from Dark Energy
Camera (DECam) and Visible and Infrared Survey Telescope for Astronomy (VISTA)
data. The DES Deep Fields comprise 11 fields (10 DES supernova fields plus
COSMOS), with a total area of $\sim30~$ square degrees in $ugriz$ bands and
reaching a maximum $i$-band depth of 26.75 (AB, $10\sigma$, 2"). We present a
catalogue for the DES 3-year cosmology analysis of those four fields with full
8-band coverage, totalling $5.88~$ sq. deg. after masking. The catalogue is
constructed in order to provide a sample of effectively noiseless galaxies (S/N
$>\sqrt{10}\times$ their equivalents in the main DES survey), to be used as a
prior on the population of objects observed in the DES and their moments in
light distribution, a source of high-quality redshift information in
constructing source galaxy redshift distributions for weak lensing analyses,
and a host of deep extragalactic science. Numbering $2.8~$million objects
($1.6~$million post masking), our catalogue is drawn from images coadded to
consistent depths of $r=25.7, i=25, z=24.3$ mag. We use a new model-fitting
code, built upon established methods, to deblend sources and ensure consistent
colours across the $u$-band to $Ks$-band wavelength range. We further detail
the tight control we maintain over the point-spread function modelling required
for the model fitting, astrometry and consistency of photometry between the
four fields. The catalogue allows us to perform a careful star-galaxy
separation and produces excellent photometric redshift performance (${\rm NMAD}
= 0.023$ at $i<23$). The Deep-Fields catalogue will be made available as part
of the cosmology data products release, following the completion of the DES
3-year weak lensing and galaxy clustering cosmology work.
