The only Final Fantasy VII-related title on PSP is Crisis Core: Final Fantasy VII (2007).
It's a prequel focusing on Zack Fair, a SOLDIER 1st Class and Cloud Strife's mentor/friend. The gameplay blends real-time action combat with RPG mechanics (DMW system, materia fusion) and significantly expands the backstory of FFVII.
Note: The original Final Fantasy VII was never released on PSP. A full remaster, Crisis Core: Final Fantasy VII Reunion, launched in 2022 for PS4/PS5, Xbox One/Series, Switch, and PC.