Shortview:
When trying to log in via iOS Certificate Wizard I receive message like "wrong username/password" and alert on iPhone "Someone accessing your Apple ID from New York etc.".
There is two buttons - "Allow" and "Disallow", but when I press "Allow" iPhone shows one-time password and asks me to enter it. Where should I enter this or is there any bypass?
P.S.: Tried using application password (generated at Apple ID profile management page) but without any result.
Currently the Certificate Wizard doesn't support two factor authentication. This issue is marked for version 3.7 (due in June).
In order to use the CertificateWizard, for now, you'll need to turn off 2-factor auth. This article describes how to do it.