You have declared your script element outside your click handler, so it is being reused, Move the var s
declaration inside the handler to get the effect you want. Like so:
$(document).ready(function () {
var AddButton = $("#AddMoreBox"); //Add button ID
var FieldCount = 0; //to keep track of text box added
$(AddButton).click(function (e) //on add input button click
{
var s = document.createElement("script");
FieldCount++; //text box added increment
s.type = "text/javascript";
s.text = '$(function(){alert(' + FieldCount + ')});';
$("head").append(s);
x++; //text box increment
return false;
});
});