Hi ,
Refer the Below Articles links also refer the below code for your reference.
- Display No results found message (No match found message) in jQuery AutoComplete
HTML 
Default.aspx 
Enter search term:
<input type="text" id="txtSearch" />
<div>
    <style type="text/css">
        body
        {
            font-family: Arial;
            font-size: 10pt;
        }
    </style>
    <script src="http://ajax.aspnetcdn.com/ajax/jQuery/jquery-1.10.0.min.js" type="text/javascript"></script>
    <script src="http://ajax.aspnetcdn.com/ajax/jquery.ui/1.9.2/jquery-ui.min.js" type="text/javascript"></script>
    <link href="http://ajax.aspnetcdn.com/ajax/jquery.ui/1.9.2/themes/blitzer/jquery-ui.css"
        rel="Stylesheet" type="text/css" />
    <script type="text/javascript">
        $(function () {
            $("[id*=txtSearch]").autocomplete({
                source: function (request, response) {
                    $.ajax({
                        url: 'Default.aspx/GetSearchResults',
                        data: "{ 'prefix': '" + request.term + "'}",
                        dataType: "json",
                        type: "POST",
                        contentType: "application/json; charset=utf-8",
                        success: function (data) {
                            if (data.d.length > 0) {
                                response($.map(data.d, function (item) {
                                    return {
                                        label: item,
                                        val: item
                                    };
                                }))
                            } else {
                                response([{ label: 'No results found.', val: -1}]);
                            }
                        }
                    });
                },
                select: function (e, u) {
                    if (u.item.val == -1) {
                        return false;
                    }
                }
            });
        });
    </script>
</div>
Code 
Default.aspx.cs 
[System.Web.Services.WebMethod]
[System.Web.Script.Services.ScriptMethod()]
public static string[] GetSearchResults(string prefix)
{
    List<string> searchResult = new List<string>();
    using (SqlConnection conn = new SqlConnection())
    {
        conn.ConnectionString = ConfigurationManager.ConnectionStrings["constr"].ConnectionString;
        using (SqlCommand cmd = new SqlCommand())
        {
            cmd.CommandText = @"SELECT FirstName Result FROM Employees
                                WHERE FirstName like @SearchText + '%'
                                UNION ALL
                                SELECT City Result FROM Employees
                                WHERE City Like @SearchText + '%'
                                UNION ALL
                                SELECT HomePhone Result FROM Employees
                                WHERE HomePhone like '%' + @SearchText + '%'";
            cmd.Parameters.AddWithValue("@SearchText", prefix);
            cmd.Connection = conn;
            conn.Open();
            using (SqlDataReader sdr = cmd.ExecuteReader())
            {
                while (sdr.Read())
                {
                    searchResult.Add(sdr["Result"].ToString());
                }
            }
            conn.Close();
        }
    }
    return searchResult.ToArray();
}
Screenshot
