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We present a new galaxy cluster search in the COSMOS field through the use ofthe Adaptive Matched Identifier of Clustered Objects (AMICO). We produced a newcluster and group catalogue up to $z=2$, by performing an innovativeapplication of AMICO with respect to previous successful applications towide-field surveys, in terms of depth (down to $r < 26.7$), small area covered($1.69 deg^2$ of unmasked area) and redshift extent. This sample, and thecomparative analysis we performed with the X-rays, allowed for the calibrationof mass-proxy scaling relations up to $z=2$ and down to less than $10^{13}M_{sun}$ and constitutes the base for the refinement of the cluster model forfuture applications of AMICO, like the analysis of upcoming Euclid data. AMICOis based on an optimal linear matched filter and detects clusters inphotometric galaxy catalogues using galaxy location, photometric redshift and,in the simplest case, one galaxy property. We used one magnitude as galaxyproperty, avoiding explicit use of galaxy colour, and performed 3 independentruns in the r, Y and H bands using both COSMOS2020 and COSMOS2015 galaxycatalogues. The final catalogue resulting from matching the results of thethree runs contains 1269 and 666 candidate clusters with $S/N >3.0$ and $>3.5$,respectively. Most of the unmatched ones have $S/N <3.5$ which can be chosen ascut for a more robust sample. We assigned X-ray properties to our detectionsvia matching with a public X-ray group sample and by estimating, for unmatcheddetections, X-ray properties at the location of AMICO candidates based onChandra+XMM-Newton data. 622 are the candidates with X-ray flux estimate. Thislarge sample allowed for the calibration of the scaling relations between AMICOmass-proxies and X-ray mass and the study of their redshift dependence for theselection of the most stable photometric bands.

AMICO-COSMOS galaxy cluster and group catalogue up to $z = 2$: Sample properties and X-ray counterparts