Please refer this example. Here i have used RequiredFieldValidator inside UserControl.
HTML
<%@ Register Src="~/UserControls/WebUserControl.ascx" TagName="UserControl" TagPrefix="uc" %>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head runat="server">
    <title></title>
    <style type="text/css">
        body
        {
            font-family: Arial;
            font-size: 10pt;
        }
    </style>
</head>
<body>
    <form id="form1" runat="server">
    <asp:GridView ID="GridView1" HeaderStyle-BackColor="#3AC0F2" HeaderStyle-ForeColor="White"
        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:TemplateField HeaderText="Address">
                <ItemTemplate>
                    <uc:UserControl ID="UserControl1" runat="server" />
                </ItemTemplate>
            </asp:TemplateField>
        </Columns>
    </asp:GridView>
    <asp:Button Text="Save" runat="server" />
    </form>
</body>
</html>
UserControl
 
<%@ Control Language="C#" AutoEventWireup="true" CodeFile="WebUserControl.ascx.cs"
    Inherits="UserControls_WebUserControl" %>
<asp:TextBox ID="txtAddress" runat="server" />
<asp:RequiredFieldValidator runat="server" ControlToValidate="txtAddress" ErrorMessage="Required"
    Display="Dynamic" ForeColor="Red"></asp:RequiredFieldValidator>
 
Namespace
using System.Data;
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();
    }
}
Screenshot
