During a barbecue, some smoke got into my mouth even while I was trying to not breathe or cover my mouth. I didnt feel it go down the same way smoking a cigarette would feel, i just felt the burning sensation in the top part of the throat. Is my fast broken by “inhaling” smoke?

Ustadh AbdulAziz al-Haqqan

No, u did not intend this whatsoever from what I habe understood from your question.