Depending on the recipe and your needs, the substitutions may vary.
The following substitutions are to replace 1 EGG
1) 1/4 cup of Mayo (refer below)
2) 1 tablespoon whole flaxseeds + 4 tablespoons water (or other liquid) processed together until blended well.
3) 1 teaspoon cornstarch, 3 tablespoons vegetable oil and a 1/4 teaspoon baking powder.
4) 1/4 cup Applesauce (a little won't add much flavor)
5) 1 Tbsp. Chia Seeds ground and mixed with 3 Tbsp. Water. Let it sit for few minutes until it gets goopy (similar to egg yolk texture)
If you are avoiding Eggs altogether for personal reasons, then don't use MAYO since Mayo is made using eggs. Choose from other substitutes.
Try this recipe for a skillet Cheddar and Jalapeno Cornbread
that's moist and a great addition to your family dinner table.