Call server side method and clients side method

I think you can. althogh you will have to decide which one will be executed first.

1. create the dropdown
2. handle the change event on client side and call a function like OnChange();
3. in this onchange function call your client side function.
4. in the same function call the server side function using XMLHttpRequet or jQuery AJAX.

the following article already decribes how to call server side function

AJAX for beginners (Part 2) - Using XMLHttpRequest and jQuery AJAX to implement a cascading dropdown[^]

I suggest you make a small change like: [Code snippet from above article, refer that for details.]

function onChange()
{ 
    //call your client side method here
   
    //create the ajax request to call server side method
    $.ajax
    ( 
        {
            type: "POST", //HTTP method
            url: "Default2.aspx/OnContinentChange", //page/method name
            data: "{'continentName':'"+$('#drpContinent').val() +"'}", //json to represent argument
            contentType: "application/json; charset=utf-8", 
            dataType: "json",
            success: callback,
            error: onError
        }
    );

}