Filter GridView with TextBox using SqlDataSource FilterExpression containing Apostrophe (Single Quote) in ASP.Net)

Here I have created sample that full fill your requirement.

HTML

<div>
    Search Customer:
    <asp:TextBox ID="txtSearch" runat="server"></asp:TextBox>
    <asp:Button ID="btnSearch" runat="server" Text="Search" OnClick="Search" />
    <hr />
    <asp:GridView ID="GridView1" HeaderStyle-BackColor="#3AC0F2" HeaderStyle-ForeColor="White"
        runat="server" AutoGenerateColumns="false" DataSourceID="GridDataSource" AllowPaging="true">
        <Columns>
            <asp:BoundField DataField="ContactName" HeaderText="Name" ItemStyle-Width="150" />
            <asp:BoundField DataField="City" HeaderText="City" ItemStyle-Width="150" />
            <asp:BoundField DataField="Country" HeaderText="Country" ItemStyle-Width="150" />
        </Columns>
    </asp:GridView>
    <asp:SqlDataSource ID="GridDataSource" runat="server" ConnectionString="<%$ ConnectionStrings:ConStr %>">
    </asp:SqlDataSource>
</div>

C#

protected void Page_Load(object sender, EventArgs e)
{
    if (!this.IsPostBack)
    {
        SearchCustomers();
    }
}

protected void Search(object sender, EventArgs e)
{
    SearchCustomers();
}

private void SearchCustomers()
{
    string value = txtSearch.Text;
    value = value.Replace("'", "['']");
    GridDataSource.SelectCommand = "SELECT ContactName, City, Country FROM Customers WHERE  (ContactName LIKE '" + value.ToString() + "%')";
}

Screenshot