In this work, we present the analysis of 976814 FGKM dwarf and subgiant stars in the Transiting Exoplanet Survey Telescope (TESS) full frame images (FFIs) of the Southern ecliptic hemisphere. We present a new pipeline, DIAmante, developed to extract optimized, multisector photometry from TESS FFIs and a classifier, based on the Random Forest technique, trained to discriminate plausible transiting planetary candidates from common false positives. A new statistical model was developed to provide the probability of correct identification of the source of variability. We restricted the planet search to the stars located in the least crowded regions of the sky and identified 396 transiting planetary candidates among which 252 are new detections. The candidates' radius distribution ranges between 1R_{Earth}_ and 2.6R_J_ with median value of 1R_J_ and the period distribution ranges between 0.25 and 105d with median value of 3.8d. The sample contains four long period candidates (P>50d), one of which is new, and 64 candidates with periods between 10 and 50d (42 new ones). In the small planet radius domain (4R<R_{Earth}_), we found 39 candidates among which 15 are new detections. Additionally, we present 15 single transit events (14 new ones), a new candidate multiplanetary system, and a novel candidate around a known TOI. By using Gaia dynamical constraints, we found that 70 objects show evidence of binarity. We release a catalogue of the objects we analysed and the corresponding light curves and diagnostic figures through the MAST and ExoFOP portals.