Q about AVCC and AGND

I am using an analog joystick with 10K potentiomenters to control both motors - using analog inputs on GPIO3 & 4.

Should I connects to potentiometers to 3.3V & GND on pins 1 & 2 or to AVcc and AGND?

I am seeing a lot of noise on 3.3V and as a result the motors keep spinning at a slow speed when the joystick is in neutral position.

Also, is there an easy method to create a dead zone in the neutral position so that vel_setpoint is 0 unless the joystick moves by a certain amount?

Thanks,

Anil