The correct answer is: no article.
The word “only” in the sentence “The only jazz musician I like is Miles Davis” indicates that the speaker is referring to a specific jazz musician, and not just any jazz musician. Therefore, we do not need to use an article before the noun “jazz musician.”
If we were to use an article, it would imply that the speaker is referring to a general category of jazz musicians, rather than a specific individual. For example, if we said “The only jazz musician I like is a trumpet player,” we would be saying that we like all trumpet players, not just Miles Davis.
In this case, the speaker is clearly referring to a specific individual, so we do not need to use an article.