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The KiDS Strongly lensed QUAsar Detection project (KiDS-SQuaD) aims atfinding as many previously undiscovered gravitational lensed quasars aspossible in the Kilo Degree Survey. This is the second paper of this serieswhere we present a new, automatic object classification method based on machinelearning technique. The main goal of this paper is to build a catalogue ofbright extragalactic objects (galaxies and quasars), from the KiDS Data Release4, with a minimum stellar contamination, preserving the completeness as much aspossible, to then apply morphological methods to select reliablegravitationally lensed (GL) quasar candidates. After testing some of the mostused machine learning algorithms, decision trees based classifiers, we decidedto use CatBoost, that was specifically trained with the aim of creating asample of extragalactic sources as clean as possible from stars. We discuss theinput data, define the training sample for the classifier, give quantitativeestimates of its performances, and finally describe the validation results withGaia DR2, AllWISE, and GAMA catalogues. We have built and make available to thescientific community the KiDS Bright EXtraGalactic Objects catalogue(KiDS-BEXGO), specifically created to find gravitational lenses. This is madeof $\approx6$ millions of sources classified as quasars ($\approx 200\,000$)and galaxies ($\approx 5.7$M), up to $r<22^m$. From this catalog we selected'Multiplets': close pairs of quasars or galaxies surrounded by at least onequasar, presenting the 12 most reliable gravitationally lensed quasarcandidates, to demonstrate the potential of the catalogue, which will befurther explored in a forthcoming paper. We compared our search to the previousone, presented in the first paper from this series, showing that employing amachine learning method decreases the stars-contaminators within the GLcandidates.

KiDS-SQuaD II: Machine learning selection of bright extragalactic objects to search for new gravitationally lensed quasars