The code is mentioned below:

<apex:page>
  <!-- 
        /**
         * Webkul Software.
         *
         * @category  Webkul
         * @author    Webkul
         * @copyright Copyright (c) 2010-2016 Webkul Software Private Limited (https://webkul.com)
         * @license   https://store.webkul.com/license.html
         */
     -->
  <apex:includeScript value="https://ajax.aspnetcdn.com/ajax/jQuery/jquery-1.7.2.min.js"/>
  <script>
    jQuery(document).ready(function($) {
      // Get Accounts via the REST API
      $.ajax('/services/data/v39.0/query?q=SELECT+Name+FROM+Account+LIMIT+10',
        {
          beforeSend: function(xhr) {
            // Set the OAuth header from the session ID
            xhr.setRequestHeader('Authorization', 'Bearer {!$Api.Session_ID}');
          },
          success: function(response) {
            // Append the records to HTML list
            $.each(response.records, function(index, record) {
              $('#accountList').append('<li>'+record.Name+'</li>');
            });
          },
          error: function(jqXHR, textStatus, errorThrown) {
            // Error
            alert(jqXHR.status + ': ' + errorThrown);
          }
        }
      );
    });
  </script>
  <h1>Test REST API</h1>
  <div>Accounts list:</div>
  <ul id="accountList">
  </ul>
</apex:page>

That’s all for how to fetch the records through REST API in visualforce page using jquery, still have any issue feel free to add a ticket and let us know your views to make the code better https://webkul.uvdesk.com/en/customer/create-ticket/