The best replacement for fpse is psx4droid.

The best alternatives to fpse are rated as following:
★★★★★  psx4droid
★★★★★  epsxe
★★★  psxperia
★★  retroarch
★  psx4all
★  webdav
★  psx

Your alternative for fpse is not listed? Suggest!
Speaking about fpse, one probably shouldn't forget about lucky patcher.

Other search terms related to fpse and their ratings are:
★★★★★ lucky patcher
★★★ sixaxis
★★ moga
★ audio and video plugins
You have in mind a companion for fpse and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of fpse in all years. Click on graph for more.
fpse
psx4droid
epsxe