Hi  manionasp,
Inorder to bind the data in gridview first you need to bind a dummy row to the GridView to access in jQuery.
Check this example. Now please take its reference and correct your code.
HTML
<div class="container">
    <asp:GridView ID="GridView1" runat="server" AutoGenerateColumns="false" CssClass="w3-table-all w3-hoverable"
        HeaderStyle-BackColor="#FFCCCC" Width="100%" ClientIDMode="Static">
        <Columns>
            <asp:TemplateField HeaderText="ID">
                <ItemTemplate>
                    <asp:Label ID="lblaid" runat="server" Text='<%#Eval("EID") %>'> </asp:Label>
                </ItemTemplate>
            </asp:TemplateField>
            <asp:TemplateField HeaderStyle-Font-Names="Arial" HeaderStyle-Font-Size="12px" HeaderStyle-ForeColor="Black"
                HeaderText="Employee Name">
                <ItemTemplate>
                    <asp:Label ID="lblagenda" runat="server" Font-Bold="True" Font-Names="Arial" Font-Size="12px"
                        Text='<%#Eval("Name") %>'>
                    </asp:Label>
                </ItemTemplate>
                <HeaderStyle Font-Names="Arial" Font-Size="12px" ForeColor="white" />
            </asp:TemplateField>
            <asp:TemplateField HeaderStyle-Font-Names="Arial" HeaderStyle-Font-Size="12px" HeaderStyle-ForeColor="Black"
                HeaderText="Email">
                <ItemTemplate>
                    <asp:Label ID="lblfid" runat="server" Font-Bold="True" Font-Names="Arial" Font-Size="12px"
                        Text='<%#Eval("Email") %>'>
                    </asp:Label>
                </ItemTemplate>
                <ControlStyle Width="100px" />
                <HeaderStyle Font-Names="Arial" Font-Size="12px" ForeColor="white" />
            </asp:TemplateField>
            <asp:TemplateField HeaderStyle-Font-Names="Arial" HeaderStyle-Font-Size="12px" HeaderStyle-ForeColor="Black"
                HeaderText="City">
                <ItemTemplate>
                    <asp:Label ID="lblgname" runat="server" Font-Bold="True" Font-Names="Arial" Font-Size="12px"
                        Text='<%#Eval("City") %>'>
                    </asp:Label>
                </ItemTemplate>
            </asp:TemplateField>
            <asp:TemplateField HeaderStyle-Font-Names="Arial" HeaderStyle-Font-Size="12px" HeaderStyle-ForeColor="Black"
                HeaderText="State">
                <ItemTemplate>
                    <asp:Label ID="lblgid" runat="server" Font-Bold="True" Font-Names="Arial" Font-Size="12px"
                        Text='<%#Eval("State") %>'>
                    </asp:Label>
                </ItemTemplate>
                <HeaderStyle Font-Names="Arial" Font-Size="12px" ForeColor="white" />
            </asp:TemplateField>
            <asp:TemplateField HeaderStyle-Font-Names="Arial" HeaderStyle-Font-Size="12px" HeaderStyle-ForeColor="Black"
                HeaderText="Country">
                <ItemTemplate>
                    <asp:Label ID="lblstatus" runat="server" Font-Bold="True" Font-Names="Arial" Font-Size="12px"
                        Text='<%#Eval("Country") %>'>
                    </asp:Label>
                </ItemTemplate>
                <ControlStyle Width="100px" />
                <HeaderStyle Font-Names="Arial" Font-Size="12px" ForeColor="white" />
            </asp:TemplateField>
            <asp:TemplateField HeaderStyle-Font-Names="Arial" HeaderStyle-Font-Size="12px" HeaderStyle-ForeColor="Black"
                HeaderText="Contact">
                <ItemTemplate>
                    <asp:Label ID="lblduedate" runat="server" Font-Bold="True" Font-Names="Arial" Font-Size="12px"
                        Text='<%#Eval("Contact") %>'>
                    </asp:Label>
                </ItemTemplate>
                <ControlStyle Width="100px" />
                <HeaderStyle Font-Names="Arial" Font-Size="12px" ForeColor="white" />
            </asp:TemplateField>
        </Columns>
        <HeaderStyle BackColor="#4dc3ff" />
        <EmptyDataTemplate>
            No Record Available
        </EmptyDataTemplate>
    </asp:GridView>
</div>
<script type="text/javascript" src="https://code.jquery.com/jquery-1.10.2.js"></script>
<link rel="stylesheet" href="https://cdn.datatables.net/1.10.12/css/jquery.dataTables.min.css" />
<link rel="stylesheet" href="https://cdn.datatables.net/buttons/1.2.2/css/buttons.dataTables.min.css" />
<script src="http://ajax.aspnetcdn.com/ajax/jQuery/jquery-1.10.2.min.js" type="text/javascript"></script>
<script type="text/javascript" src="https://cdn.datatables.net/1.10.12/js/jquery.dataTables.min.js"></script>
<script type="text/javascript" src="https://cdn.datatables.net/buttons/1.2.2/js/dataTables.buttons.min.js"></script>
<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/jszip/2.5.0/jszip.min.js"></script>
<script type="text/javascript" src="https://cdn.rawgit.com/bpampuch/pdfmake/0.1.18/build/pdfmake.min.js"></script>
<script type="text/javascript" src="https://cdn.rawgit.com/bpampuch/pdfmake/0.1.18/build/vfs_fonts.js"></script>
<script type="text/javascript" src="https://cdn.datatables.net/buttons/1.2.2/js/buttons.html5.min.js"></script>
<script type="text/javascript">
    $(document).ready(function () {
        $.ajax({
            type: "POST",
            url: '<%=ResolveUrl("Default.aspx/GetEmployees") %>',
            dataType: "json",
            data: {},
            contentType: "application/json",
            success: function (data) {
                displayTable(data.d);
            },
            error: function (result) {
                alert("Error login");
            }
        });
    });
    function displayTable(data) {
        $('#GridView1').prepend($("<thead></thead>").append($(this).find("tr:first"))).DataTable({
            data: JSON.parse(data),
            "columns": [
                    { "data": "EID" },
                    { "data": "Name" },
                    { "data": "Email" },
                    { "data": "City" },
                    { "data": "State" },
                    { "data": "Country" },
                    { "data": "Contact" }
                ]
        });
    }
</script>
C#
protected void Page_Load(object sender, EventArgs e)
{
    if (!IsPostBack)
    {
        System.Data.DataTable dt = new System.Data.DataTable();
        dt.Columns.AddRange(new System.Data.DataColumn[]{
            new System.Data.DataColumn("EID", typeof(int)),
            new System.Data.DataColumn("Name", typeof(string)),
            new System.Data.DataColumn("Email", typeof(string)),
            new System.Data.DataColumn("City",typeof(string)),
            new System.Data.DataColumn("State", typeof(string)),
            new System.Data.DataColumn("Country", typeof(string)),
            new System.Data.DataColumn("Contact", typeof(string))});
        dt.Rows.Add();
        GridView1.DataSource = dt;
        GridView1.DataBind();
    }
}
[System.Web.Services.WebMethod(EnableSession = true)]
public static string GetEmployees()
{
    System.Data.DataTable dt = new System.Data.DataTable();
    dt.Columns.AddRange(new System.Data.DataColumn[]{
            new System.Data.DataColumn("EID", typeof(int)),
            new System.Data.DataColumn("Name", typeof(string)),
            new System.Data.DataColumn("Email", typeof(string)),
            new System.Data.DataColumn("City",typeof(string)),
            new System.Data.DataColumn("State", typeof(string)),
            new System.Data.DataColumn("Country", typeof(string)),
            new System.Data.DataColumn("Contact", typeof(string))});
    for (int i = 1; i < 4000; i++)
    {
        dt.Rows.Add(i, "Robert Frank", "test1@test.com", "Los Angeles", "California", "United States", "N/A");
    }
    string JSONString = string.Empty;
    JSONString = Newtonsoft.Json.JsonConvert.SerializeObject(dt);
    return JSONString;
}
Screenshot
