For Card Orders:
Technically, the system does not allow you to ask for a refund because you have the option of canceling the order, as long as you do it before the card is charged.
Nevertheless, refunds are issued:
If the payment transaction flow is not completed entirely
If the risk engine flags your transaction after the card is charged
This engine makes automatic evaluations of all transactions. In rare cases of a transaction being flagged after the card is charged, the order will be rejected, a refund will automatically be issued and you will be notified via email.
NOTE: In case a refund has been issued, it might take a few extra days for the funds to reach your account and it depends entirely on bank processing times.
For Bank Orders:
You can easily cancel the order before sending the bank transfer to Coinify. These orders can be canceled from the 'Trade History' section in your myCoinify account, or from the 'Order History' menu in your Blockchain wallet.
Trade History in myCoinify account:
If you want to cancel some of your orders, please, click on the order under question and then click on "Cancel trade" in the bottom left corner of the page.
Order History in the Blockchain Wallet:
However, the cancellation of your bank order/orders has no effect once the bank transfer has been sent. The order will be processed and the Bitcoins you purchased will be delivered accordingly.
Additionally, there are cases when Coinify will not process Bank Orders and will issue a refund instead. Bear in mind that Administrative Fees will be applied! Read more about the cases when Coinify does not process Bank Orders here.