Adding a dead zone to a analog imput on arduino Leonardo

Joystick.setXAxis(map(analogRead(A3),0,1023,-127,127));

Rather than directly using the built-in 'map()' function you could define a custom function:

int readAxis(byte pin)
{
  int v = analogRead(pin);

  if (v < deadRangeLow)
    return map(v ,0, deadRangeLow, -127, 0);

  if (v > deadRangeHi)
    return map(v, deadRangeHigh, 1023, 0, 127));

  return 0;
}

Then you can just use:

Joystick.setXAxis(readAxis(A3));

If you ever need to change the mapping you only need to do it in one place.