Hello @manionasp,
Below is the code example. just try it! 
<%@ Page Language="C#" AutoEventWireup="true" CodeFile="Datatable.aspx.cs" Inherits="Datatable" %>
<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head runat="server">
    <title>Data Table Plugin</title>
    <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/4.0.0-beta/css/bootstrap.css" />
    <link rel="stylesheet" href="https://cdn.datatables.net/1.10.16/css/dataTables.bootstrap4.min.css" />
    <link rel="stylesheet" href="https://cdn.datatables.net/responsive/2.1.1/css/responsive.bootstrap4.min.css" />
</head>
<body>
    <form id="form1" runat="server">
        <div class="container">
            <div class="row">
                <div class="col-lg-12">
                    <asp:GridView ID="GridView1" runat="server" CssClass="table table-bordered"></asp:GridView>
                </div>
            </div>
        </div>
    </form>
    <script src="https://code.jquery.com/jquery-3.3.1.min.js"></script>
    <script src="https://cdn.datatables.net/1.10.16/js/jquery.dataTables.min.js"></script>
    <script src="https://cdn.datatables.net/1.10.16/js/dataTables.bootstrap4.min.js"></script>
    <script src="https://cdn.datatables.net/responsive/2.1.1/js/dataTables.responsive.min.js"></script>
    <script src="https://cdn.datatables.net/responsive/2.1.1/js/responsive.bootstrap4.min.js"></script>
    <script type="text/javascript">
        $(function () {
            $('[id$=GridView1]').prepend($("<thead></thead>").append($('[id$=GridView1]').find("tr:first"))).DataTable({
                "responsive": true,
                "sPaginationType": "full_numbers"
            });
        });
    </script>
</body>
</html>
 
using System;
using System.Collections.Generic;
using System.Data;
using System.Linq;
using System.Web;
using System.Web.UI;
using System.Web.UI.WebControls;
public partial class Datatable : System.Web.UI.Page
{
    protected void Page_Load(object sender, EventArgs e)
    {
        BindGrid();
    }
    private void BindGrid()
    {
        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();
    }
}