When ever you do the mousemove, it is checking the condition and attaching the click event. So the click event is attached many times. To avoid this, first remove the click event using off('click')
and attach it. Here is the updated fiddle.
var widthScreen = $(window).width();
$(document).on('mousemove', function(e) {
console.log(e.pageX);
if (e.pageX > (widthScreen - 120) && e.pageX < widthScreen) {
$('ul').addClass('right-show');
$('li').eq(2).off('click').on('click', function() {
console.log('too much click');
});
} else {
$('ul').removeClass('right-show');
}
});