If you can no longer complete the second verification step, the knowledge base says you need to disable 2-factor authentication / 2-step verification first, then regain access.
What to do:
1. Follow the reset instructions for 2-factor authentication if it is configured.
2. The terminology depends on DSM version:
- DSM 7.0 and above and DSM Enterprise: 2-factor authentication
- DSM 6.2 and earlier: 2-step verification
If the problem is specifically with your Synology Account:
- Check whether you can recover it using a recovery phone (SMS) or a recovery code.
- If none of the backup methods are available and you cannot sign in, Synology Support must verify your identity and manually deactivate MFA.
Related notes from the knowledge base:
- If your account is temporarily locked because of too many failed login attempts, wait and try again later, or follow the instructions in the email sent to your primary email address.
- If you cannot sign in because of a verification code issue, make sure the code from the Synology Secure SignIn app is entered before it expires.
Sources used: [10], [11], [12], [13]