The scope of the project 'A PSF-based Approach to TESS High Quality data Of Stellar clusters' (PATHOS) is the extraction and analysis of high-precision light curves of stars in stellar clusters and young associations for the identification of candidate exoplanets and variable stars. The cutting-edge tools used in this project allow us to measure the real flux of stars in dense fields, minimizing the effects due to contamination by neighbour sources. We extracted about 200000 light curves of stars in 645 open clusters located in the Southern ecliptic hemisphere and observed by TESS during the first year of its mission. We searched for transiting signals and we found 33 objects of interest, 11 of which are strong candidate exoplanets. Because of the limited SNR, we did not find any Earth or super-Earth. We identified two Neptune-size planets orbiting stars with R*<1.5R_{sun}_, implying a frequency f*=1.3+/-0.95 per cent consistent with the frequency around field stars. The seven Jupiter candidates around stars with R*<1.5R_{sun}_ imply a frequency f*=0.19+/-0.07 per cent, which is smaller than in the field. more complete estimate of the survey completeness and false positive rate is needed to confirm these results. Light curves used in this work will be made available to the astronomical community on the Mikulski Archive for Space Telescope under the project PATHOS.