Hi indradeo,
Please refer below sample code.
Database
For this example I have used of Northwind database that you can download using the link given below.
Download Northwind Database
HTML
<div>
    <div class="modal fade" id="myModal" role="dialog">
        <div class="modal-dialog">
            <!-- Modal content-->
            <div class="modal-content">
                <div class="modal-header">
                    <button type="button" class="close" data-dismiss="modal">
                        ×</button>
                    <h4 class="modal-title">Requst Details</h4>
                </div>
                <div class="modal-body">
                    <div class="col-lg-12 col-sm-12 col-md-12 col-xs-12">
                        <div class="form-group">
                            <font size='2'>
                            <b>ID :</b> <asp:Label ID="Id" runat="server" Text="Id"></asp:Label> <br /><br />
                            <b>Employee Id : </b><asp:Label ID="EmpCode" runat="server" Text="EmpCode"></asp:Label>
                            </font>
                        </div>
                        <font size='2'>
                                <div class="form-group">
                                <b>Asset Type : </b> <asp:Label ID="asst_typ" runat="server" Text=""></asp:Label>
                                </div>
                            </font>
                    </div>
                    <font size='2'>
                        <div class="form-group">
                        <b>Location : </b><asp:Label ID="lcn" runat="server" Text="lcn"></asp:Label> ,
                        <b>Purpose : </b><asp:Label ID="prps" runat="server" Text="prps"></asp:Label><br /><br />
                        <b>Remark : </b><asp:Label ID="rmk" runat="server" Text="rmk"></asp:Label>
                        </div>
                    </font>
                    <font size='2'>
                    <div class="form-group">
                    <b>Asset Status : <asp:dropdownlist id="ddlTest" runat="server" AutoPostBack="true" OnSelectedIndexChanged="DropDownList_Changed" >
                    <asp:ListItem Text="--Select Country --" Value="C" />
                    <asp:ListItem Text="USA" Value="USA" />
                    <asp:ListItem Text="UK" Value="UK" />
                    </asp:dropdownlist>      
                    <b>Intalation date : </b><asp:TextBox ID="TextBox2" runat="server"></asp:TextBox>
                    </b><br /><br />
                    <b>Asset Serial No. : </b><asp:TextBox ID="TextBox3" runat="server"></asp:TextBox>
                    <br /><br />
                    <b>Remark : </b><asp:TextBox ID="TextBox1" runat="server" width="300px"></asp:TextBox>
                        </div>
                </font>
                </div>
                <div class="modal-footer">
                    <asp:Button ID="btnSave" runat="server" Text="Save" ToolTip='Click here to Save Data' CssClass="btn btn-info" />
                    <asp:Button ID="btnchk" runat="server" Text="Send" ToolTip='Click here to Check Asset Details' CssClass="btn btn-info" />
                    <button type="button" class="btn btn-info" data-dismiss="modal">
                        Close</button>
                </div>
            </div>
        </div>
    </div>
    <script type='text/javascript'>
        function openModal() {
            $('[id*=myModal]').modal('show');
        }
    </script>
</div>
Namespace
C#
using System.Data;
using System.Configuration;
using System.Data.SqlClient;
VB.Net
Imports System.Data
Imports System.Configuration
Imports System.Data.SqlClient
Code
C#
protected void Page_Load(object sender, EventArgs e)
{
    if (!this.IsPostBack)
    {
        ClientScript.RegisterStartupScript(this.GetType(), "Popup", "openModal();", true);
    }
}
protected void DropDownList_Changed(object sender, EventArgs e)
{
    TextBox1.Visible = false;
    TextBox2.Visible = false;
    TextBox3.Visible = false;
    if (ddlTest.SelectedItem.Value == "USA" || ddlTest.SelectedItem.Value == "UK")
    {
        string conString = ConfigurationManager.ConnectionStrings["constr"].ConnectionString;
        string query = "SELECT * FROM Employees WHERE Country = @Country";
        using (SqlConnection con = new SqlConnection(conString))
        {
            using (SqlCommand cmd = new SqlCommand(query, con))
            {
                cmd.Parameters.AddWithValue("@Country", ddlTest.SelectedItem.Value);
                using (SqlDataAdapter sda = new SqlDataAdapter(cmd))
                {
                    using (DataTable dt = new DataTable())
                    {
                        sda.Fill(dt);
                        TextBox1.Text = dt.Rows[0]["Notes"].ToString();
                        TextBox2.Text = Convert.ToDateTime(dt.Rows[0]["BirthDate"]).ToShortDateString();
                        TextBox3.Text = dt.Rows[0]["EmployeeId"].ToString();
                        TextBox1.Visible = true;
                        TextBox2.Visible = true;
                        TextBox3.Visible = true;
                    }
                }
            }
        }
    }
    ClientScript.RegisterStartupScript(this.GetType(), "Popup", "openModal();", true);
}
VB.Net
Protected Sub Page_Load(ByVal sender As Object, ByVal e As EventArgs) Handles Me.Load
    If Not Me.IsPostBack Then
        ClientScript.RegisterStartupScript(Me.GetType(), "Popup", "openModal();", True)
    End If
End Sub
Protected Sub DropDownList_Changed(ByVal sender As Object, ByVal e As EventArgs) Handles Me.Load
    TextBox1.Visible = False
    TextBox2.Visible = False
    TextBox3.Visible = False
    If ddlTest.SelectedItem.Value = "USA" OrElse ddlTest.SelectedItem.Value = "UK" Then
        Dim conString As String = ConfigurationManager.ConnectionStrings("constr").ConnectionString
        Dim query As String = "SELECT * FROM Employees WHERE Country = @Country"
        Using con As SqlConnection = New SqlConnection(conString)
            Using cmd As SqlCommand = New SqlCommand(query, con)
                cmd.Parameters.AddWithValue("@Country", ddlTest.SelectedItem.Value)
                Using sda As SqlDataAdapter = New SqlDataAdapter(cmd)
                    Using dt As DataTable = New DataTable()
                        sda.Fill(dt)
                        TextBox1.Text = dt.Rows(0)("Notes").ToString()
                        TextBox2.Text = Convert.ToDateTime(dt.Rows(0)("BirthDate")).ToShortDateString()
                        TextBox3.Text = dt.Rows(0)("EmployeeId").ToString()
                        TextBox1.Visible = True
                        TextBox2.Visible = True
                        TextBox3.Visible = True
                    End Using
                End Using
            End Using
        End Using
    End If
    ClientScript.RegisterStartupScript(Me.GetType(), "Popup", "openModal();", True)
End Sub
Screenshot
