Hi @Anonymous ,
You cannot create new controls on screen dynamically.
Although in your scenario as you say you want to add parts then you can do the following:
Method 1: Use of Collection -> Work with collections to store parts for Parent Record.
When you click on add new part, then create a new record in Collection.
Use this collection in Gallery (which contains your controls) -> The number of records will determine parts requested.
Therefore, if you have multiple controls (Textboxes, Labels, etc) will get repeated with every record.
Method 2: You can create a new Blank Record directly to your datasource by filling only required data and patch function.
Hopefully you have Textbox control in Gallery connected, as you add new record, you will get next set of controls.
Hope this helps