This depends on your fasting goal. If it's fat loss you’re after, you should be fine with a stick or two during your fast. If you’re looking to achieve autophagy (cell cleaning) you want to steer clear. That’s because chewing automatically activates digestive juices and consequently the body prepares for food intake.
Plus, candies and chewing gum often contain sugar or artificial sweeteners, increasing insulin levels and breaking the fast. To play it safe, better to chew your gum during your eating window and go for the natural types containing stevia.