Most psx games run perfectly if you convert to an eboot for PSP, if you just want that system's games on a handheld.
If it's just that you have a 3ds and wanted to use them on that... then well.. don't hold your breath.. look for ports of the games.. like Chrono Trigger or Dragon Warrior/Quest 7. (yes i realize Ct is actually a Super Nintendo game originally, but there was a PSX version between that and the DS version, and now steam version)