A PSF-based Approach to TESS High quality data Of Stellar clusters
  (PATHOS) -- II. Search for exoplanets in open clusters of the southern
  ecliptic hemisphere and their frequency
  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, minimising the effects due to contamination by neighbour sources. We
extracted about 200 000 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 them are strong candidate exoplanets. Because of the limited
S/N, we did not find any Earth or super-Earth. We identified two Neptune-size
planets orbiting stars with $R_{\star}<1.5\,R_{\odot}$, implying a frequency
$f_{\star}=1.34 \pm 0.95\,\%$, consistent with the frequency around field
stars. The 7 Jupiter candidates around stars with $R_{\star}<\,1.5R_{\odot}$
imply a frequency $f_{\star}=0.19\pm 0.07\,\%$, smaller than in the field. A
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.
