JSFiddle - React, Tailwind, and code Playground

HTML

<script src="http://ajax.googleapis.com/ajax/libs/jqueryui/1.11.4/jquery-ui.js"></script>
<br><br><br><br><br><br>
datepicker 1<br>
<input type="text" class="datepicker"><br><br>

<div class="outer">
    <div class="inner"><br><br><br><br><br><br>
        datepicker 2(inside fixed div)<br>
        <input type="text" class="datepicker">
        <br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /> <span>end of inner div</span>
    </div>
</div>
<br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br>

CSS

.outer
{
    position: fixed;
    background: #ddd; 
    width: 100%;
    height: 500px;
    padding: 20px;
}

.inner
{
    position: fixed;
    background: #fff; 
    width: 80%;
    height: 200px;
    overflow-y: scroll;
}

JavaScript

$(".datepicker").datepicker();