Hi, thank you for reaching out. I’m happy to help.
I understand that you are receiving the message 'Please retry with a different device or other authentication method to sign in' when trying to log in. This usually appears due to unusual activity, a high volume of requests, or similar issues.
First, I suggest that you reset your password and try again: https://account.live.com/ResetPassword.aspx
If the issue persists, make sure you’re using a device and location you’ve previously used to sign in. Try using a different verification method, such as an alternate email instead of SMS (or vice versa). Avoid making repeated attempts. In some cases, waiting 24 hours may help resolve the issue.
Reference: See the 'Try another verification method' section: