Onclick event are not working properly

on click event in node.js is not working but simple text input work.i want that when you click on buttons( in my case two buttons) the two different event happen but it does not work. these two different events are append DOM within page. one of the button have value 'X' and other one have 'O' and i want to just append DOM with button's value. How can i do that? this is code--->

my script is-

        $(function() {


            var socket = io.connect(window.location.href);


            socket.on('message:server', function(data) {
                $("#messages").append(
                    '<li style="color:red">' +
                    data.message + ' - ' + 'received' + ' ' + new Date() +
                    '</li>'
                );
            });


            $("#message_form").on('submit', function(event) {


                event.preventDefault();


                var $input = $('[name="message"]')
                var message = $input.val();


                if (message) {
                    socket.emit('message:client', {message: message});
                }


                $("#messages").append(
                    '<li style="color:green">' + 
                    message + ' - ' + 'sent' + ' ' + new Date() +
                    '</li>'
                );


                $input.val('');
            });


            socket.on('error', function() {
                console.error(arguments)
            });
        });

in Body tag- 

    <form id="message_form" method="post">
        <input name="message" placeholder="Message to send" type="text"/>
        <button type="submit">Submit</button>
    </form>

here at bottom in place of form i want 2 buttons which can operate this with default given fix value.

What about creating two buttons in the DOM and calling .on('click', function(){}) instead of submit ?

Like :

<button id="value1">Send value 1</button>
<button id="value2">Send value 2</button>

Then you simply set the function on click event. I added comments to your code to show what you can remove :

$("#value1").on('click', function(event) {

  event.preventDefault();

  // var $input = $('[name="message"]');
  // You don't need fix since you send "fixed" value
  var message = "Value 1" // Or whatever you want instead of $input.val();

  // if (message) {
  // No need of condition since you set the value
  socket.emit('message:client', {message: message});
  // }

  $("#messages").append(
    '<li style="color:green">' + 
    message + ' - ' + 'sent' + ' ' + new Date() +
    '</li>'
  );

  // $input.val('');
});

You simply do the same for your button 2. For this example, you would call : 

$('#value2').on('click', function(){ 
  // Same as value with another message value
});