New colour-cut criteria (black dotted line) defined by Eq. (6) applied to EDF-N. In grey we show all Euclid compact sources that have a DESI counterpart. The blue coloured points represent the Euclid compact sources selected as DESI BLQSO candidates and the red ones represent the Euclid compact objects selected as galaxy candidates by DESI. Moreover, the purple lines represent the 68% (solid) and 95% (dashed) contours of the stellar candidates found in Sect. 3.1.