It’s the same for children, and anxiety in children and young people is very common. There are a lot of things you can do to help and encouraging your child to face their fears is one of them. I don’t mean throw them in at the deep end, but acknowledge that their fear is real to them, and then encourage baby steps towards overcoming that fear.
So, if you have a child who is scared of dogs take them somewhere where you know there will be dogs and just watch from a safe distance to start with (or even just watch some cute pu then gradually increase this challenge until your child can stand next to you on the path while a dog walks past, then move on to the next step etc. Remember to praise your child for facing up to their fears. If you have an anxious child, this sort of support is important and will help to make a difference.