Hi  DPrasad,
Make the method as public with static and remember to decorate the method with WebMethod in order to call with jQuey Ajax.
Like below.
    [WebMethod]
    public static void InsertLogOutTime()
    {
        string ip = "";
        string AT = "";
        if (Session["ip"] != "" || Session["ip"] != null)
        {
            ip = Session["ip"].ToString();
        }
        else
        {
            ip = "N/A";
        }
 
        if (Session["arrivalTime"] != "" || Session["arrivalTime"] != null)
        {
            AT = Session["arrivalTime"].ToString();
        }
        else
        {
            AT = "N/A";
        }
        
        string constr = ConfigurationManager.ConnectionStrings["CS"].ConnectionString;
        string sqlStatment = string.Format(@"INSERT INTO [dbo].[VISIT_DURATION]([IP_ADDRESS]
                   ,[LEAVING_TIME]
                   ,[ARRIVAL_TIME]) VALUES(@ip,@LeavingTime,@ArrivalTime)");
        using (SqlConnection con = new SqlConnection(constr))
        {
            using (SqlCommand cmd = new SqlCommand(sqlStatment, con))
            {
                con.Open();
                cmd.Parameters.AddWithValue("@ip", ip.ToString());
                cmd.Parameters.AddWithValue("@LeavingTime", DateTime.Now.ToLongTimeString());
                cmd.Parameters.AddWithValue("@ArrivalTime", AT.ToString());
 
                cmd.ExecuteNonQuery();
                con.Close();
            }
        }
    }
Also make sure the page name in the url: "saveLeavingTime.aspx/InsertLogOutTime", is correct.