I would like to sell bbq on side road
If you are in NYC then this may be regulated. Frequently however in many places this would be regulated by the county you reside in. Contact the local health dept. They can tell you where to go and who to contact.
You will likely need a business license and I suspect they are stiffer with home kitchens than commercial kitchens. If you have indoor pets, you might not get licensed at all.