HTML tag <a> want to add both href and onclick working

You already have what you need, with a minor syntax change:

<a href="www.mysite.com" onclick="return theFunction();">Item</a>

<script type="text/javascript">
    function theFunction () {
        // return true or false, depending on whether you want to allow the `href` property to follow through or not
    }
</script>

The default behavior of the <a> tag's onclick and href properties is to execute the onclick, then follow the href as long as the onclick doesn't return false, canceling the event (or the event hasn't been prevented)

Use jQuery. You need to capture the click event and then go on to the website.

$("#myHref").on('click', function() {
  alert("inside onclick");
  window.location = "http://www.google.com";
});

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<a href="#" id="myHref">Click me</a>

To achieve this use following html:

<a href="www.mysite.com" onclick="make(event)">Item</a>

<script>
    function make(e) {
        // ...  your function code
        // e.preventDefault();   // use this to NOT go to href site
    }
</script>

Here is working example.