First thing I want to clarify here, this question is because of curiosity. I am not facing any issue.
There are many primitive types available in Java byte
You all are wrong. Yes. You can. As a rule, you do not need a completely new primitive type. So, you don't need to rebuild JVM. Usually, you only need to "pack" or "cast" your new primitive type to an existing and define some operations like "+" with its wrapper.
You can do it relatively simply with original JVM, but with your own Java compiler. Good luck!