ASP.NET - Passing a C# variable to HTML
All of this is assuming that this is just a textbox somewhere on your page, rather than in a DataBound control. If the textbox is part of an itemTemplate in a repeater, and Child_ID is something that differes by data row, then all of this is incorrect.
Do this instead:
<asp:TextBox ID="TextBoxChildID" runat="server" Enabled="false"><%= Child_ID %></asp:TextBox>
In short, you're making the same mistake I was making when I asked this question: Why <%= %> works in one situation but not in another
Alternatively, in code-behind, you can have this in your ASPX:
<asp:TextBox ID="TextBoxChildID" runat="server" Enabled="false"></asp:TextBox>
and this in your Code-Behind:
TextBoxChildID.Text = Child_ID;
The variable must be public first. And:
'<%# Child_ID %>'