First of all, you must understand that UITableViewCell and UITextField are just views, they are not supposed to hold data, they are just supposed to display them and allow the user to interact with them: The data should remain stored in the controller of the table view.
You have to remember that UITableView allows you to reuse UITableViewCell instances for performance purpose: what's displayed on the screen are actually the only subviews UITableView keep there. It means that you'll reuse one cell that already has a text field in it and set the text on that field directly. When the user will tap on the field it will edit it and you'll have to get the value back from it when the user will have finished.
The fastest way, would be to use what Satya proposes, that is building normal UITableViewCell and insert into a UITextField (there's no need for a CustomTextField class...). The tag will allow you to get back to the text field easily... But you'll have to setup your text field so it behaves properly when the table view resizes or if a label in the same cell changes.
The cleanest way to do that is to subclass UITableViewCell and setup the layout of your label and text field, and you can provide the text field as a property of the custom subclass.