Here I would like to code how to create the searchable Dropdown list using Asp.net and JQuery .I have used a Plugin to operate this functionality you can download plugin from this LINK  or else you can copy paste the code to your javascript file(.js)

<html>
<head>
    <script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.8.3/jquery.min.js"></script>
    <script src="Scripts/jquery.searchabledropdown-1.0.8.min.js" type="text/javascript"></script>
    <script type="text/javascript">
 $(document).ready(function () {
   $("select").searchable({
      maxListSize: 200, // if list size are less than maxListSize, show them all
      maxMultiMatch: 300, // how many matching entries should be displayed
      exactMatch: false, // Exact matching on search
      wildcards: true, // Support for wildcard characters (*, ?)
      ignoreCase: true, // Ignore case sensitivity
      latency: 200, // how many millis to wait until starting search
      warnMultiMatch: 'top {0} matches ...',
      warnNoMatch: 'no matches ...',
      zIndex: 'auto'
          });
       });

    </script>
</head>
<body>
    <form id="form1" runat="server">
        <asp:DropDownList ID="myselect" runat="server">
            <asp:ListItem>Select</asp:ListItem>
            <asp:ListItem>venki</asp:ListItem>
            <asp:ListItem>venu</asp:ListItem>
            <asp:ListItem>charles ven</asp:ListItem>
            <asp:ListItem>venuzila</asp:ListItem>
            <asp:ListItem>veron philender</asp:ListItem>
            <asp:ListItem>india</asp:ListItem>
            <asp:ListItem>indianven</asp:ListItem>
            <asp:ListItem>vesta</asp:ListItem>
        </asp:DropDownList>
    </form>
</body>
</html>