If I've got the layout of the data structure right, it is a key/value object, which in turn contains objects that have information such as connected.
In that case you can use Object.keys to get the keys first, sort those Object.keys(data).sort(), and create the html from there. For example:
function showClients(data) {
    var html = Object.keys(data).sort().reduce(function(h, clientId){
        return h + '<p>' + clientId
        + (data[clientId].connected ? ' connected' : ' disconnected')
        + '</p>';
    }, '')
        || '<p>No clients connected</p>';
    $('#connected_clients').html(html);
}
function showClients(data) {
    var html = Object.keys(data).sort().reduce(function(h, clientId){
     return h + '<p>' + clientId
        + (data[clientId].connected ? ' connected' : ' disconnected')
        + '</p>';
    }, '')
     || '<p>No clients connected</p>';
    
    $('#connected_clients').html(html);
}
showClients({Client3:{connected:true},Client1:{connected:true},Client2:{connected:false}});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<div id=connected_clients></div>