What type of connector is on the mouse? PS2? USB?
How are you trying to connect it to the Amiga? USB card (Highway/Algor/Subway, Spider, Thycyline?) or through the serial port? Or do you have a dedicated PS2/serial mouse adapter for the Amiga's standard mouse port?
I have both an optical Logitech mouse as well as an optical Logitech trackball hooked up to my Amiga and both work well.
The mouse is hooked up to the PS2 mouse adapter Mr. Mysa to the Amiga's mouse port and works like a charm, even with hardware banging older games. The only limitation I've found is that Mr. Mysa doesn't like mouse/joypad switchers.
The trackball on the other hand is plugged into my Highway USB card and performs great under Poseidon with system friendly apps.