Is there one? For example, "Bill was a hipster who only enjoyed [very strange and specialized genres of] music".
I think the meaning is (a) well-known, and (b) has a wide application, so I will skip the definitions.
It is specifically applicable, given your description. The New American Dictionary states:
Obscure often expresses dissatisfaction at one's inability to identify something.
genre itself is specific (or specialised1), and that you are going to give a [specific] genre is the expectation of the listener.
You are trying to identify a genre, but you can't. So you want to express all that in one word.
Bill was a hipster who only enjoyed obscure music
Bill was a hipster who only enjoyed recherché music
The foreign word is foreign, unknown, obscure (sorry). You will have to stop and explain what it means to the other person.
- Your title 'specialized genre' is redundant because genre is specific. Your description is completely understood.