1. What does it mean?
피셜 is clipped from 오피셜 and used after a source, as in 본인피셜 or 친구피셜. It marks whose statement you are repeating, sometimes seriously and sometimes with mock authority.
Also written or said as pisyeol
2. The nuance
The source may be informal or mistaken. 친구피셜 is not the same as independently verified information, and 뇌피셜 deliberately highlights personal speculation.
3. Examples
“친구피셜로는 입구가 두 군데래. 안내도도 확인하자.”
According to my friend there are two entrances. Let's check the map too.
“본인피셜, 이번 주에는 쉬면서 새 노래를 준비한대.”
By their own account, they're resting this week while preparing a new song.
Sources
References support the meaning and usage. Example sentences are written for NoCapWiki.