The eROSITA telescope aboard the Spectrum Roentgen Gamma (SRG) satellite provides an unprecedented opportunity to explore the transient and variable extragalactic X-ray sky due to the sensitivity, sky coverage, and cadence of the all-sky survey. While previous studies showed the dominance of regular active galactic nuclei (AGN) variability, a small fraction of sources expected in such a survey arise from more exotic phenomena such as tidal disruption events (TDEs), quasi-periodic eruptions, or other short-lived events associated with supermassive black hole accretion. This paper describes the systematic selection of X-ray extragalactic transients found in the first two eROSITA all-sky surveys (eRASS) that are not associated with known AGN prior to eROSITA observations. We generated a variability sample using the data from the first and second eRASS, which includes sources with a variability significance and a fractional amplitude larger than four in the 0.2--2.3 keV energy band. The sources were discovered between December 2019 and December 2020, and are located in the Legacy Survey DR10 (LS10) footprint. When possible, transients were associated with optical LS10 counterparts. The properties of these counterparts were used to exclude stars and known active galaxies. The sample was additionally cleaned from known AGN using pre-eROSITA SIMBAD and the Million Quasars Catalog (Milliquas) classifications, archival optical spectra, and archival X-ray data. We explored archival X-ray variability, long-term (2--2.5 years) eROSITA light curves, and peak X-ray spectra to characterize the X-ray properties of the sample. Sources with radio counterparts were identified using the Rapid ASKAP Continuum Survey (RACS) and the Karl G. Jansky Very Large Array Sky Survey (VLASS). We present a catalog of 304 extragalactic eROSITA transients and variables not associated with known AGN, called eRO-ExTra. More than 90\,&lt;!PCT!&gt; of sources are associated with reliable LS10 optical counterparts. For each source, we provide archival X-ray data from swift ros and xmm ; the eROSITA long-term light curve with a light curve classification; as well as the best power law fit spectral results at the peak eROSITA epoch. Reliable spectroscopic and photometric redshifts, which are both archival and from follow-up data, are provided for more than 80\,&lt;!PCT!&gt; of the sample. Several sources in the catalog are known TDE candidates discovered by eROSITA. In addition, 31 sources are radio detected. The origin of radio emission needs to be further identified. The eRO-ExTra transients constitute a relatively clean parent sample of non-AGN variability phenomena associated with massive black holes. The eRO-ExTra catalog includes more than 95\,&lt;!PCT!&gt; of sources discovered in X-rays with eROSITA for the first time, which makes it a valuable resource for studying unique nuclear transients.

eRO-ExTra: eROSITA extragalactic non-AGN X-ray transients and variables in eRASS1 and eRASS2