  A complete and pure sample of quasars with accurate redshifts is crucial for
quasar studies and cosmology. In this paper, we present CatNorth, an improved
Gaia DR3 quasar candidate catalog with more than 1.5 million sources in the
3$\pi$ sky built with data from Gaia, Pan-STARRS1, and CatWISE2020. The XGBoost
algorithm is used to reclassify the original Gaia DR3 quasar candidates as
stars, galaxies, and quasars. To construct training/validation datasets for the
classification, we carefully built two different master stellar samples in
addition to the spectroscopic galaxy and quasar samples. An ensemble
classification model is obtained by averaging two XGBoost classifiers trained
with different master stellar samples. Using a probability threshold of
$p_{\mathrm{QSO\_mean}}>0.95$ in our ensemble classification model and an
additional cut on the logarithmic probability density of zero proper motion, we
retrieved 1,545,514 reliable quasar candidates from the parent Gaia DR3 quasar
candidate catalog. We provide photometric redshifts for all candidates with an
ensemble regression model. For a subset of 89,100 candidates, accurate
spectroscopic redshifts are estimated with the Convolutional Neural Network
from the Gaia BP/RP spectra. The CatNorth catalog has a high purity of ~ 90%
while maintaining high completeness, which is an ideal sample to understand the
quasar population and its statistical properties. The CatNorth catalog is used
as the main source of input catalog for the LAMOST phase III quasar survey,
which is expected to build a highly complete sample of bright quasars with $i <
19.5$.
