  Context: the theory of stellar evolution presents shortcomings when
confronted with asteroseismic probes of interior physical properties. The
differences between observations and theory are often great because stellar
models have mainly been calibrated from observables connected to the surface of
stars. Period-spacing patterns caused by gravity modes are a particularly
powerful asteroseismic tool that are useful for probing the near-core rotation
and mixing of chemical elements in main-sequence stars with convective cores.
Aims: we aim to compose a catalog of intermediate-mass stars in the TESS
southern continuous viewing zone to reveal period-spacing patterns caused by
gravity modes for use in future asteroseismic modeling. Methods: TESS full
frame images were inspected to select stars of intermediate- and high-mass
using color-magnitude criteria. Light curves were extracted from custom masks
per star, adopting stringent constraints on the aperture masks and
contamination. The extracted light curves were subject to iterative
prewhitening to detect gravity modes. We developed a method based on the
assumption that period spacings are an approximately linear function of the
mode periods to build a template pattern. This template was used to extract the
patterns and their bootstrap uncertainties. Results: our TESS catalog of
high-quality period-spacing patterns is the first of its kind and contains 140
gravity-mode patterns in 106 Gamma Doradus stars and 2 slowly pulsating B-type
stars. Half of these patterns contain 7 or more measured mode periods and the
longest pattern contains 20 modes. We provide the community with a convenient
software tool to search for period-spacing patterns and to process the
extracted light curves. Conclusions: our catalog offers a fruitful starting
point for future gravity-mode asteroseismology of rotating dwarfs with
convective cores in the southern hemisphere.
