Get Current Session Value in JavaScript?

Another approach is in your chtml

<input type="hidden" id="hdnSession" data-value="@Request.RequestContext.HttpContext.Session['someKey']" />

  and the script is

var sessionValue= $("#hdnSession").data('value');

or you may access directly by

 jQuery(document).ready(function ($) {
        var value = '@Request.RequestContext.HttpContext.Session["someKey"]';
    }); 

The session is a server side thing, you cannot access it using jQuery. You can write an Http handler (that will share the sessionid if any) and return the value from there using $.ajax.