The JWST Advanced Deep Extragalactic Survey (JADES) is a multi-cycle JWST program that has taken among the deepest near-infrared images to date (down to $\sim$30.5 ABmag) over $\sim$25 arcmin$^2$ in the GOODS-S field in two sets of observations with one year of separation. This presented the first opportunity to systematically search for transients, mostly supernovae (SNe), out to $z>$2. We found 79 SNe: 38 at $z<$2, 23 at 2$Comment: 43 pages, 15 figures, 15 tables. Submitted to ApJ. Appendix A (64 MB) is available at https://drive.google.com/file/d/1xs5jXUVOvdDPgdghK72KR1FMGvPcK7dv/view?usp=sharing . Appendix B (81 MB) is available at https://drive.google.com/file/d/18ImLT80pQdPzXCZA-KEy21DaE2CQiGz1/view?usp=sharing . References updated