The project Seen in Liberty City by Barcode Studia is a major fan-made remake that effectively serves as a "fixed" port for the PSP
: Advanced users can leverage plugins to upscale resolution up to 8x on devices like the PS Vita or mobile, turning a 20-year-old game into a modern-feeling handheld title. GTA 3 Definitive Is It Fixed? Performance Review
A fixed port of GTA III on the PSP would likely require significant development effort, optimization, and testing. While it is theoretically feasible, there are several challenges and limitations to consider. Rockstar Games and Sony have not officially announced any plans to re-release GTA III on the PSP or any other handheld console.
Yes—if you are a tinkerer, a GTA completionist, or a retro handheld enthusiast.