The preposition "on" is optional in both sentences, but using it slightly changes the tone. Here’s how each option works:
With "on":
"She was puffing on a cigarette at the time."
"I sat puffing on my cigar."
Using "on" gives a bit more focus to the ongoing action and can add a casual, conversational feel. It’s common in informal English and is slightly more descriptive, emphasizing the act of smoking.
Without "on":
"She was puffing a cigarette at the time."
"I sat puffing my cigar."
Without "on," the sentences are still correct, but the phrasing sounds a bit more concise or formal. This version focuses more directly on the action without the additional emphasis on the process.
Both versions are grammatically correct, so it’s really a matter of personal preference and tone. For a more conversational feel, use "on"; for a more straightforward style, you can omit it.