With its first All-Sky Survey (eRASS1), the extended ROentgen Survey with an Imaging Telescope Array (eROSITA) on board the Spectrum-Roentgen-Gamma (SRG) mission has offered an unprecedented, comprehensive view of the variable X-ray sky. Featuring enhanced sensitivity, broader energy coverage, and improved resolution compared to prior surveys, the eRASS1 Data Release 1 (DR1) catalogue underwent a variability analysis, and in this paper, we performed an advanced variability analysis focusing on a substantial subset of 128 669 sources, all exhibiting a net count exceeding ten. We performed multiple variability tests, utilising conventional normalised excess variance (NEV), maximum amplitude variability (AMP), and Bayesian excess variance methods (bexvar). The analysis focused on binned light curves; specifically, employing one eroday (a great circle scan with a duration of 4 hours) binning of the German part of the first eROSITA all-sky survey (eROSITA-DE) data, i.e., the source sample covers only half of the sky. Within the 128 669 DR1 sources with light curves, our research pinpointed 808 light curves that show hints of variability according to the AMP test, and 298 according to the NEV test. However, after applying suitable thresholds, 90 (123) sources were found to be significantly variable according to the AMP (NEV) tests. In addition, 1342 sources are considered variable according to the Bayesian test bexvar. The total number of unique sources is 1709, and they form the catalogue of variable sources released with this paper. We cross-matched with existing X-ray catalogues and identified 258, 318, 598, and 120 sources in 4XMM DR13, 2SXPS, 2RXS, and CSC2.1, respectively. Only 27 sources overlap across all catalogues, while 882 are new X-ray detections from eROSITA DR1. About 70% are coronal stars, 5% are Quasi-Stellar Objects, and 1.6% are normal galaxies. We further subclassified 18 sources as LMXBs, 11 as HMXBs, and 14 as bright stars. In this paper, we analyse the variability of eRASS1 sources on a timescale of only a few days. To study the physics of variable sources, we need more deeply pointed observations with other X-ray missions or at least the final depth of the eRASS: 8 observations. The timescale of the eRASS1 observations is not representative of the timescales of the expected upcoming eRASS catalogues. A substantial 52% of the eRASS1 variable sources were first discovered with eROSITA. The DR1 variability catalogue is excellent for follow-up observations with telescopes such as XMM-Newton, Chandra, or Swift.