Some Playstation games will not work with analog turned on, in ePSXe you can tap F5 to toggle this on/off

Pressing the analog button on the pad does not change the settings in the emulator, hence pressing F5 does that instead

Best to keep analog on the pad itself set to on

Make sure the pad is hooked up before you start the emulator

It is mostly the older games that don't support analog though

I would also stick to the corded controllers I can't see the adapters working with wireless controllers