Hi EmadKhan,

If you want to fetch the data asynchronously then you need to code at client side using jquery or other option is using update panel.

I have used Northwind database Customers and Orders table records for sample you can get database from below article.

Install the Northwind and Pubs Sample Databases in SQL Server Express

Refer below sample code and modify it according to your need.

HTML

<div>
    <asp:DropDownList ID="ddlCustomers" runat="server">
    </asp:DropDownList>
    <br />
    <span class="card-data-title">OrderID:&nbsp;<label id="lblOrderID" class="billDesc"></label></span>
    <br />
    <span class="card-data-title">Freight:&nbsp;<label id="lblFreight" class="billAmount"></label></span>
</div>
<div>
    <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/jquery/1.8.3/jquery.min.js"></script>
    <script type="text/javascript">
        $(function () {
            $('[id*=ddlCustomers]').change(function () {
                var customerId = $(this).val();
                $.ajax({
                    type: "POST",
                    contentType: "application/json; charset=utf-8",
                    url: '<%=ResolveUrl("Default.aspx/GetOrderDetail") %>',
                    data: '{"customerId": "' + customerId + '"}',
                    dataType: "json",
                    success: function (response) {
                        $('[id*=lblOrderID]').html('');
                        $('[id*=lblFreight]').html('');
                        var xml = $.parseXML(response.d);
                        var orderDetail = $(xml).find("OrderDetail");
                        var orderId = $(orderDetail).find("OrderID").text();
                        var freight = $(orderDetail).find("Freight").text();
                        $('[id*=lblOrderID]').html(orderId);
                        $('[id*=lblFreight]').html(freight);
                    },
                    error: function (a, b, c) {
                        alert(a.responseText);
                    }
                });
            });
        });
    </script>
</div>

C#

protected void Page_Load(object sender, EventArgs e)
{
    if (!this.IsPostBack)
    {
        string constr = ConfigurationManager.ConnectionStrings["constr"].ConnectionString;
        using (SqlConnection con = new SqlConnection(constr))
        {
            using (SqlCommand cmd = new SqlCommand("SELECT TOP 10 CustomerID,ContactName FROM Customers", con))
            {
                using (SqlDataAdapter sda = new SqlDataAdapter(cmd))
                {
                    DataTable dt = new DataTable();
                    sda.Fill(dt);
                    ddlCustomers.DataSource = dt;
                    ddlCustomers.DataTextField = "ContactName";
                    ddlCustomers.DataValueField = "CustomerID";
                    ddlCustomers.DataBind();
                    ddlCustomers.Items.Insert(0, (new ListItem("Please Select", "")));
                }
            }
        }
    }
}

[System.Web.Services.WebMethod]
public static string GetOrderDetail(string customerId)
{
    string constr = ConfigurationManager.ConnectionStrings["constr"].ConnectionString;
    SqlConnection con = new SqlConnection(constr);
    SqlCommand cmd = new SqlCommand("SELECT TOP 1 OrderID ,Freight FROM Orders WHERE CustomerID = @CustomerID", con);
    cmd.Parameters.AddWithValue("@CustomerID", customerId);
    SqlDataAdapter sda = new SqlDataAdapter(cmd);
    DataTable dt = new DataTable("OrderDetail");
    sda.Fill(dt);
    DataSet ds = new DataSet();
    ds.Tables.Add(dt);
    return ds.GetXml();
}

VB.Net

Protected Sub Page_Load(sender As Object, e As EventArgs) Handles Me.Load
    If Not Me.IsPostBack Then
        Dim constr As String = ConfigurationManager.ConnectionStrings("constr").ConnectionString
        Using con As New SqlConnection(constr)
            Using cmd As New SqlCommand("SELECT TOP 10 CustomerID,ContactName FROM Customers", con)
                Using sda As New SqlDataAdapter(cmd)
                    Dim dt As New DataTable()
                    sda.Fill(dt)
                    ddlCustomers.DataSource = dt
                    ddlCustomers.DataTextField = "ContactName"
                    ddlCustomers.DataValueField = "CustomerID"
                    ddlCustomers.DataBind()
                    ddlCustomers.Items.Insert(0, (New ListItem("Please Select", "")))
                End Using
            End Using
        End Using
    End If
End Sub

<System.Web.Services.WebMethod()> _
Public Shared Function GetOrderDetail(customerId As String) As String
    Dim constr As String = ConfigurationManager.ConnectionStrings("constr").ConnectionString
    Dim con As New SqlConnection(constr)
    Dim cmd As New SqlCommand("SELECT TOP 1 OrderID ,Freight FROM Orders WHERE CustomerID = @CustomerID", con)
    cmd.Parameters.AddWithValue("@CustomerID", customerId)
    Dim sda As New SqlDataAdapter(cmd)
    Dim dt As New DataTable("OrderDetail")
    sda.Fill(dt)
    Dim ds As New DataSet()
    ds.Tables.Add(dt)
    Return ds.GetXml()
End Function

ScreenShot