There are several chemical compositions which will produce fairly copious amounts of smoke with just a couple of drops being mixed.
These, naturally, can be a bit foul smelling on the one hand, and even dangerous when inhaled on the other.
If you can be more specific about exactly how you want to use the smoke, whether you're producing animals from it (etc.), and whether or not you're in a well-ventilated area, I might be able to make some recommendations. I created chemical smoke out of various noxious compounds when a teenage magician. Much of the stuff I used, if you're not a chemist or in the medical field, would be much harder to get today, I suspect.
A couple of the instant smoke-from sleeve or real smoke at fingertip gimmicks advertised in magic magazines over the last decade or so actually contained very dangerous chemicals which should not have been used for the purposes described. Several performers lost sleeves on expensive tuxedo jackets and worse.