* A derogatory term for a cheap or poorly written article. This would play on the idea of a puff piece, which is a flattering or exaggerated article, and the low-quality association with newspaper.
* An attempt to describe a specific type of cigarette. This is unlikely, but it's possible someone might use it metaphorically to describe a cigarette rolled with newspaper paper, which would be extremely unhealthy and uncommon.
* A slang term used in a particular geographic location or community. The phrase might have a unique meaning in a specific region or group.
To help me understand what you mean by "puff on newspaper," please provide more context. For example:
* Where did you encounter this phrase?
* What was the overall topic of the conversation?
* What did you think it meant?
With more information, I can give you a more accurate answer.