  This paper presents a new search for $z\geq7.5$ galaxies using the COSMOS2020
photometric catalogues. Finding galaxies at the reionization epoch through deep
imaging surveys remains observationally challenging. The larger area covered by
ground-based surveys like COSMOS enables the discovery of the brightest
galaxies at these high redshifts. Covering $1.4$deg$^2$, our COSMOS catalogues
were constructed from the latest UltraVISTA data release (DR4) combined with
the final Spitzer/IRAC COSMOS images and the Hyper-Suprime-Cam Subaru Strategic
Program DR2 release. We identify $17$ new $7.5<z<10$ candidate sources, and
confirm $15$ previously published candidates. Using deblended photometry
extracted by fitting surface brightness models on multi-band images, we select
four candidates which would be rejected using fixed aperture photometry. We
test the robustness of all our candidates by comparing six different
photometric redshift estimates. Finally, we compute the galaxy UV luminosity
function in three redshift bins centred at $z=8,9,10$. We find no clear
evolution of the number density of the brightest galaxies $M_\text{UV}<-21.5$,
in agreement with previous works. Rapid changes in the quenching efficiency or
attenuation by dust could explain such lack of evolution between $z\sim 8$ and
$z\sim 9. A spectroscopic confirmation of the redshifts, already planned with
JWST and the Keck telescopes, will be essential to confirm our results.
