The payment process starts with creating the payment order. There is one related payment resource created automatically with each new order (amount is equal as the amount of the whole order). Order can be updated (e.g. amount adjusted Update Order endpoint) and the behavior is based on the status of the related payment resource:
when payment has not been initialized yet - order and related payment is updated
when payment has been processed already - new payment is created and added to order
Once the order is created, it can be further processed by one of two flows:
Redirect flow (using Everifin GUI)
Embedded flow (full API flow without using Everifin GUI)
All available endpoints related to orders are described here: Orders API