Refer the below article about ajax call.

Search GridView with Paging on TextBox KeyPress using jQuery in ASP.Net

You need to check the selected radiobutton as per the condition and call the web method according to the condition.

HTML

<div>
    <label id="lsea1">
        <input type="radio" name="iCheck" id="RBmkv" runat="server" dir="rtl" />RBMKV</label>
    <label id="lsea1">
        <input type="radio" name="iCheck" id="RBdvd" runat="server" />RBDVD</label>
</div>
<div>
    <script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.8.3/jquery.min.js"></script>
    <script type="text/javascript">
        $(function () {
            $('[name=iCheck]').on('change', function () {
                var checkedRadioButton = $(this)[0].value;
                if (checkedRadioButton.toLowerCase() == "rbmkv") {
                    GetCustomers("GetCustomersPageWise", 1);
                }
                else if (checkedRadioButton.toLowerCase() == "rbdvd") {
                    GetCustomers("GetCustomersPageWisedvd", 1);
                }
            });
        });

        function GetCustomers(method, pageIndex) {
            $.ajax({
                type: "POST",
                url: "Default.aspx/" + method,
                data: '{pageIndex: ' + pageIndex + '}',
                contentType: "application/json; charset=utf-8",
                dataType: "json",
                success: function OnSuccess(response) {
                    //do your stuff.
                },
                failure: function (response) {
                    alert(response.d);
                },
                error: function (response) {
                    alert(response.d);
                }
            });
        }        
    </script>
</div>

Code

[WebMethod]
public static string GetCustomersPageWise(string pageIndex)
{
    return ""; //return as per your requirement
}

[WebMethod]
public static string GetCustomersPageWisedvd(string pageIndex)
{
    return ""; //return as per your requirement
}