You are calling
.DataBind()
after you add your custom item, which will clear the control. change the order to:
select_city();
if (DT.Columns.Count > 0)
{
drplst_City.DataSource = DT;
drplst_City.DataTextField = "Name"; drplst_City.DataValueField = "Id";
drplst_City.DataBind();
drplst_City.Items.Add(new ListItem("other", ""));
}