Reverse blade katana, also known as sakabato is a katana with the sharp edge inside of the curve, rather than on the outside, which is usually unsharpened. Though there are reports this type of sword was discovered in Japan just recently, it’s believed to be purely fictional katana and there’s no real evidence it was ever used by samurai.
Sakabato comes from the Rurouni Kenshin, a very popular anime and manga series, which is why many people are looking to buy real replicas of reverse-bladed katana.
Reverse blade katana are much harder to purchase however, especially if you’re looking for a fully functional battle ready sword: there are some available by Musashi and Masahiro. If you intend to do any cutting, make sure you get a sword with at least 1050 carbon steel blade.