1. What does it mean?
알빠노 is an internet-style dismissal of something as none of the speaker's concern. It plays on 알 바, something one needs to know or care about, and a stylized questioning ending.
Also written or said as alppano
2. The nuance
It can be jokingly defiant, but it often sounds cold or hostile. The spelling 빠 is part of the meme rather than standard 알 바, and the expression should not be treated as neutral polite Korean.
3. Examples
“친구가 진지하게 말하는데 알빠노라고 답하면 상처가 되지.”
Replying 'not my problem' when a friend is serious can hurt them.
“이 댓글의 알빠노는 농담보다 무시하는 말처럼 읽혔어.”
The 'why should I care?' in this comment read more like dismissal than a joke.
Sources
Sinjoeo Korean Slang Dictionary
References support the meaning and usage. Example sentences are written for NoCapWiki.