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. We aim to compose a catalog of intermediate-mass stars in the Transiting Exoplanet Survey Satellite (TESS) southern continuous viewing zone (CVZ) to reveal period-spacing patterns caused by gravity modes for use in future asteroseismic modeling. TESS full frame images (FFI) 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 relying 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 uncertainties, relying on a bootstrap approach. Our TESS catalog of high-quality period-spacing patterns is the first of its kind and contains 140 gravity-mode patterns in 106 {gamma} Dor stars and two slowly pulsating B-type (SPB) stars. Half of these patterns contain seven 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. Our catalog offers a fruitful starting point for future gravity-mode asteroseismology of rotating dwarfs with convective cores in the southern hemisphere.