What would you add to inter- make the meaning be existing between brothers?

The prefix "inter-" means "between" or "among." To indicate something existing between brothers, you would use the word fraternal.

Here are some examples:

* Fraternal bond: A strong connection between brothers.

* Fraternal rivalry: Competition between brothers.

* Fraternal support: The way brothers help each other.

The word "fraternal" specifically refers to brothers and is often used to describe relationships, feelings, or actions between them.