This will solve your problem. Logic is same as the solution suggested by Kyle.
Have a look at this.
<head runat="server">
<title></title>
<script type="text/javascript">
function RefreshUpdatePanel() {
__doPostBack('<%= Code.ClientID %>', '');
};
</script>
<asp:TextBox ID="Code" runat="server" onkeyup="RefreshUpdatePanel();" AutoPostBack="true" OnTextChanged="Code_TextChanged"></asp:TextBox>
<asp:UpdatePanel ID="Update" runat="server">
<ContentTemplate>
<asp:DropDownList runat="server" ID="DateList" />
<asp:TextBox runat="server" ID="CurrentTime" ></asp:TextBox>
</ContentTemplate>
<Triggers>
<asp:AsyncPostBackTrigger ControlID="Code" />
</Triggers>
</asp:UpdatePanel>
Code behind goes like this…
protected void Code_TextChanged(object sender, EventArgs e)
{
//Adding current time (minutes and seconds) into dropdownlist
DateList.Items.Insert(0, new ListItem(DateTime.Now.ToString("mm:ss")));
//Setting current time (minutes and seconds) into textbox
CurrentTime.Text = DateTime.Now.ToString("mm:ss");
}
I have added additional textbox to see change in action, do remove the textbox.