Flax Seeds or Chia Seeds (My favorite for cookies & bars) When ground flax seeds and water combine, the mixture takes on a gelatinous consistency similar to egg whites. To replace one large egg, combine 1 tablespoon of ground flax seeds with 3 tablespoons of water. Silken Tofu If other leavening agents, like baking soda or baking powder, are on your ingredients list, there's a chance eggs are only providing moisture. In that case, opt for silken tofu — ¼ cup per egg. Banana or Applesauce Like tofu, mashed banana adds a lot of moisture to batter and dough, but it won't help leaven. Baking Soda and Vinegar (My favorite for cakes) There's a science project-worthy reaction that happens when you combine baking soda and vinegar: It bubbles up, and increases in volume. That's what happens when you add it to dough or batter, too: It'll fluff up your baked goods, sort of like eggs do. Instant Mashed Potatoes In savory recipes — meatballs, meatloaf, veggie burgers — this powdered potato can serve as a good binder. Try adding 2 heaping tablespoons to your mixture. Aquafaba (Love this stuff- cookie, pies) Ignore the fancy word: This is simply the leftover liquid from a can of beans, though it doesn't taste anything like beans once it's cooked. It only acts as a replacement for egg whites, which makes it a good candidate to be used in meringues or macaroons. For every egg, use 3 tablespoons of the liquid. Nut Butter Creamy nut butters — sorry chunky fans — are one of the best ways to bind dry ingredients together without eggs. They'll vastly change the taste of your baked good. Egg Replacer Now that veganism's a thing, more and more egg replacer powders are hitting the market. Bob's Red Mill and Ener-G make theirs with tapioca flour and potato starch, while some brands use arrowroot starch or chickpea flour. Follow instructions on the package.
Reference:
https://www.delish.com/kitchen-tools/advice/g4834/vegan-egg-substitutes/