The ASAS-SN catalogue of variable stars III: variables in the southern TESS continuous viewing zone

The All-Sky Automated Survey for Supernovae (ASAS-SN) provides long baseline (${\sim}4$ yrs) light curves for sources brighter than V$\lesssim17$ mag across the whole sky. The Transiting Exoplanet Survey Satellite (TESS) has started to produce high-quality light curves with a baseline of at least 27 days, eventually for most of the sky. The combination of ASAS-SN and TESS light curves probes both long and short term variability in great detail, especially towards the TESS continuous viewing zones (CVZ) at the ecliptic poles. We have produced ${\sim}1.3$ million V-band light curves covering a total of ${\sim}1000 \, \rm deg^2$ towards the southern TESS CVZ and have systematically searched these sources for variability. We have identified ${\sim} 11,700$ variables, including ${\sim} 7,000$ new discoveries. The light curves and characteristics of the variables are all available through the ASAS-SN variable stars database (this https URL). We also introduce an online resource to obtain pre-computed ASAS-SN V-band light curves (this https URL) starting with the light curves of the ${\sim}1.3$ million sources studied in this work. This effort will be extended to provide ASAS-SN light curves for ${\sim}50\;$million sources over the entire sky.