what makes small white cocoons & squishes red?

Question

The cocoons are sticky & bug inside squishes red. They are all over the branches of barberry bushes and Japanese maple.

Answer 1

The "cocoons" are likely the bug itself. It sounds like you have either mealy bugs or wooly aphids. Here is more information about how to control both pests:
https://www.gardeningknowhow.com/plant-problems/pests/mealybugs-white-residue-on-plants-leaves.htm

https://www.gardeningknowhow.com/plant-problems/pests/insects/woolly-aphid-control.htm