Below is The Working Demo for Datepicker with Bootstrap modal

Add Below Script to add Date picker in Script Tag

 

$( function() {
  $( "#datepicker" ).datepicker();
});
$("[id=add]").click(function() {
  $("#myModal .modal-header h4").html("Request for Change");
  $("#myModal").modal("show");
});
$(".date-picker").datepicker({
  orientation: "top",
  beforeShow: function(input, obj) {
$(input).after($(input).datepicker('widget'));
  }
});
$(".date-picker").focus(function (){
  $("#ui-datepicker-div").position({
    my: "center top",
    at: "center bottom",
    of: $(this)
  });
});
.datepicker-container{
  position: relative !important;
}

Add Below Line In Header

 

<link rel="stylesheet" href="https://code.jquery.com/ui/1.12.1/themes/base/jquery-ui.css">
<script src="https://code.jquery.com/jquery-1.12.4.js"></script>
<script src="https://code.jquery.com/ui/1.12.1/jquery-ui.js"></script>
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/css/bootstrap.min.css">
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js"></script>

Add Below Line In Body:

 

<div class="well">
  <button type="button" id="add">Add</button>
</div>
<div id="myModal" class="modal">
  <div class="modal-dialog">
    <div class="modal-content">
      <div class="modal-header">
        <h4></h4>
      </div>
      <div class="modal-body">
        <label class="label">Date picker</label>
        <div class="datepicker-container">
          <input class="form-control datePicker date-picker" id="datepicker" placeholder: "MM/YYYY">
        </div>
        <h1>helllo</h1>
        <h1>helllo</h1>
        <h1>helllo</h1>
        <h1>helllo</h1>
        <h1>helllo</h1>
        <h1>helllo</h1>
        <h1>helllo</h1>
        <h1>helllo</h1>
        <h1>helllo</h1>
        <h1>helllo</h1>
        <h1>helllo</h1>
        <h1>helllo</h1>
        <h1>helllo</h1>
        <h1>helllo</h1>
        <h1>helllo</h1>
        <h1>helllo</h1>
        <h1>helllo</h1>
        <h1>helllo</h1>
        <h1>helllo</h1>
        <h1>helllo</h1>
        <h1>helllo</h1>
        <h1>helllo</h1>
        <h1>helllo</h1>
        <h1>helllo</h1>
        <h1>helllo</h1>
        <h1>helllo</h1>
        <h1>helllo</h1>
        <h1>helllo</h1>
        <h1>helllo</h1>
        <h1>helllo</h1>
      </div>
    </div>
  </div>
</div>