The census of Galactic H <small>Ⅱ</small> regions is vastly incomplete in the southern sky. We use the Australia Telescope Compact Array to observe 4-10 radio continuum and hydrogen radio recombination line (RRL) emission from candidate H <small>Ⅱ</small> regions in the Galactic zone 250° < < 344°,|b|4°. In this first data release, we target the brightest H <small>Ⅱ</small> region candidates and observe 282 fields in the direction of at least one previously known or candidate H <small>Ⅱ</small> region. We detect radio continuum emission and RRL emission in 275 (97.5%) and 258 (91.5%) of these fields, respectively. We catalog the ∼7 GHz radio continuum peak flux densities and positions of 80 previously known and 298 candidate H <small>Ⅱ</small> regions. After averaging ∼18 RRL transitions, we detect 77 RRL velocity components toward 76 previously known H <small>Ⅱ</small> regions and 267 RRL velocity components toward 256 H <small>Ⅱ</small> region candidates. The discovery of RRL emission from these nebulae increases the number of known Galactic H <small>Ⅱ</small> regions in the surveyed zone by 82% to 568 nebulae. In the fourth quadrant, we discover 50 RRLs with positive velocities, placing those sources outside the solar circle. Including the pilot survey, the Southern H <small>Ⅱ</small> Region Discovery Survey has now discovered 295 Galactic H <small>Ⅱ</small> regions. In the next data release, we expect to add ∼200 fainter and more distant nebulae.