Hi mohammedobri,

You need to set AutoCompleteExtender ServicePath to work while using routing.

Using the below two article i have created an example.

Implement URL Routing in ASP.Net Web Forms 4.0

AJAX AutoCompleteExtender Example in ASP.Net

Refer below sample code.

HTML

Default

<h1>Home</h1>
<hr />
<a href='<%=ResolveUrl("~/Customers") %>'>View Customers</a>

Customers

<asp:ScriptManager ID="ScriptManager1" runat="server" EnablePageMethods="true">
</asp:ScriptManager>
<h1>Customers</h1>
<asp:TextBox ID="txtContactsSearch" runat="server"></asp:TextBox>
<cc1:AutoCompleteExtender ServiceMethod="SearchCustomers" ServicePath="Customers.aspx"
    MinimumPrefixLength="2" TargetControlID="txtContactsSearch"
    CompletionInterval="100" EnableCaching="false" CompletionSetCount="10"
    ID="AutoCompleteExtender1" runat="server" FirstRowSelected="false">
</cc1:AutoCompleteExtender>
<hr />
<asp:GridView ID="GridView1" runat="server" AutoGenerateColumns="false">
    <Columns>
        <asp:BoundField DataField="Id" HeaderText="Id" ItemStyle-Width="30" />
        <asp:BoundField DataField="Name" HeaderText="Name" ItemStyle-Width="150" />
        <asp:BoundField DataField="Country" HeaderText="Country" ItemStyle-Width="150" />
        <asp:HyperLinkField Text="View" DataNavigateUrlFormatString="~/Customers/{0}" DataNavigateUrlFields="Id" />
    </Columns>
</asp:GridView>

CustomerDetails

<h1>Customer Details</h1>
<hr />
<b>Customer Id:</b>
<asp:Label ID="lblCustomerId" runat="server" />

Namespaces

C#

using System.Configuration;
using System.Data;
using System.Data.SqlClient;
using System.Web.Script.Services;
using System.Web.Services;

VB.Net

Imports System.Configuration
Imports System.Data
Imports System.Data.SqlClient
Imports System.Web.Script.Services
Imports System.Web.Services

Code

Customers

C#

protected void Page_Load(object sender, EventArgs e)
{
    if (!this.IsPostBack)
    {
        DataTable dt = new DataTable();
        dt.Columns.AddRange(new DataColumn[3] { new DataColumn("Id", typeof(int)),
                        new DataColumn("Name", typeof(string)),
                        new DataColumn("Country",typeof(string)) });
        dt.Rows.Add(1, "John Hammond", "United States");
        dt.Rows.Add(2, "Mudassar Khan", "India");
        dt.Rows.Add(3, "Suzanne Mathews", "France");
        dt.Rows.Add(4, "Robert Schidner", "Russia");
        GridView1.DataSource = dt;
        GridView1.DataBind();
    }
}

[ScriptMethod()]
[WebMethod]
public static List<string> SearchCustomers(string prefixText, int count)
{
    using (SqlConnection conn = new SqlConnection())
    {
        conn.ConnectionString = ConfigurationManager.ConnectionStrings["constr"].ConnectionString;
        using (SqlCommand cmd = new SqlCommand())
        {
            cmd.CommandText = "select ContactName from Customers where ContactName like @SearchText + '%'";
            cmd.Parameters.AddWithValue("@SearchText", prefixText);
            cmd.Connection = conn;
            conn.Open();
            List<string> customers = new List<string>();
            using (SqlDataReader sdr = cmd.ExecuteReader())
            {
                while (sdr.Read())
                {
                    customers.Add(sdr["ContactName"].ToString());
                }
            }
            conn.Close();
            return customers;
        }
    }
}

VB.Net

Protected Sub Page_Load(sender As Object, e As EventArgs) Handles Me.Load
    If Not Me.IsPostBack Then
        Dim dt As New DataTable()
        dt.Columns.AddRange(New DataColumn() {New DataColumn("Id", GetType(Integer)),
                                                New DataColumn("Name", GetType(String)),
                                                New DataColumn("Country", GetType(String))})
        dt.Rows.Add(1, "John Hammond", "United States")
        dt.Rows.Add(2, "Mudassar Khan", "India")
        dt.Rows.Add(3, "Suzanne Mathews", "France")
        dt.Rows.Add(4, "Robert Schidner", "Russia")
        GridView1.DataSource = dt
        GridView1.DataBind()
    End If
End Sub

<ScriptMethod()>
<WebMethod>
Public Shared Function SearchCustomers(ByVal prefixText As String, ByVal count As Integer) As List(Of String)
    Using conn As SqlConnection = New SqlConnection()
        conn.ConnectionString = ConfigurationManager.ConnectionStrings("constr").ConnectionString
        Using cmd As SqlCommand = New SqlCommand()
            cmd.CommandText = "select ContactName from Customers where ContactName like @SearchText + '%'"
            cmd.Parameters.AddWithValue("@SearchText", prefixText)
            cmd.Connection = conn
            conn.Open()
            Dim customers As List(Of String) = New List(Of String)()
            Using sdr As SqlDataReader = cmd.ExecuteReader()
                While sdr.Read()
                    customers.Add(sdr("ContactName").ToString())
                End While
            End Using
            conn.Close()
            Return customers
        End Using
    End Using
End Function

CustomerDetails

C#

protected void Page_Load(object sender, EventArgs e)
{
    if (!this.IsPostBack)
    {
        lblCustomerId.Text = this.Page.RouteData.Values["CustomerId"].ToString();
    }
}

VB.Net

Protected Sub Page_Load(sender As Object, e As EventArgs) Handles Me.Load
    If Not Me.IsPostBack Then
        lblCustomerId.Text = Me.Page.RouteData.Values("CustomerId").ToString()
    End If
End Sub

Global.asax

C#

<%@ Application Language="C#" %>
<%@ Import Namespace="System.Web.Routing" %>
<script runat="server">
    void Application_Start(object sender, EventArgs e) 
    {
        RegisterRoutes(RouteTable.Routes);
    }
    
    static void RegisterRoutes(RouteCollection routes)
    {
        routes.MapPageRoute("Customers", "Customers", "~/Customers.aspx");
        routes.MapPageRoute("CustomerDetails", "Customers/{CustomerId}", "~/CustomerDetails.aspx");
    }
</script>

VB.Net

<%@ Application Language="VB" %>
<%@ Import Namespace="System.Web.Routing" %>
<script RunAt="server">
    Private Sub Application_Start(sender As Object, e As EventArgs)
        RegisterRoutes(RouteTable.Routes)
    End Sub

    Private Shared Sub RegisterRoutes(routes As RouteCollection)
        routes.MapPageRoute("Customers", "Customers", "~/Customers.aspx")
        routes.MapPageRoute("CustomerDetails", "Customers/{CustomerId}", "~/CustomerDetails.aspx")
    End Sub
</script>

Screenshot