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
      $.ajax('/services/data/v41.0/sobjects/Account',{
          type:'POST',
          data:'{"Name":"Test Company"}',
          dataType: 'json',
          beforeSend: function(xhr) {
            // Set the OAuth header from the session ID
            xhr.setRequestHeader('Authorization', 'Bearer {!$Api.Session_ID}');            
            xhr.setRequestHeader('Content-Type', 'application/json; charset=UTF-8');
            
          },
          success: function(response) {
            // Sit the result to HTML div          
              $('[Id$=accountId]').html(JSON.stringify(response));
          },
          error: function(jqXHR, textStatus, errorThrown) {
            // Error
            alert(jqXHR.status + ': ' + errorThrown);
          }
        }
      );
      
    });
    
  </script>
  <h1>REST API (POST method)</h1>
  <div>Account Info:</div>
  <div id="accountId">
  </div>
</apex:page>

That’s all for how to send Post Request through AJAX 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/