We catalogue the 443 bright supernovae (SNe) discovered by the All-Sky Automated Survey for Supernovae (ASAS-SN) in 2018-2020 along with the 519 SNe recovered by ASAS-SN and 516 additional mpeak <= 18 mag SNe missed by ASAS-SN. Our statistical analysis focuses primarily on the 984 SNe discovered or recovered in ASAS-SN g-band observations. The complete sample of 2427 ASAS-SN SNe includes earlier V-band samples and unrecovered SNe. For each SN, we identify the host galaxy, its UV to mid-IR photometry, and the SN's offset from the centre of the host. Updated peak magnitudes, redshifts, spectral classifications, and host galaxy identifications supersede earlier results. With the increase of the limiting magnitude to g <= 18 mag, the ASAS-SN sample is nearly complete up to mpeak = 16.7 mag and is 90 per cent complete for mpeak <= 17.0 mag. This is an increase from the V-band sample, where it was roughly complete up to mpeak = 16.2 mag and 70 per cent complete for mpeak <= 17.0 mag.