Unfortunately we do not offer a way to manage (create, edit, delete) custom ticketing attributes through the API. The API will only allow you to change which attributes are available for each ticket.
Custom attributes are managed in Admin -> Tickets -> Attributes. Here you can create attributes, choose the type (dropdown, textbox, etc.), create the choices (if applicable), and set the associated ticket types.
If you have any questions about attributes or how certain fields work, feel free to ask here in the questions system and I will help out any way I can!