Both Uses

nevertheless
in
Harry Potter (#2) and the Chamber of Secrets
(Edited)

Slightly dizzy, he nevertheless kept his eyes wide open, rain was speckling his glasses and ran up his nostrils as he hung upside down, avoiding another fierce dive from the Bludger.
p. 170.8 *

nevertheless = still (used to connect contrasting ideas)
And while Harry was sure he had never heard the name T. M. Riddle before, it still seemed to mean something to him, almost as though Riddle was a friend he'd had when he was very small, and had half-forgotten. He'd never had friends before Hogwarts, Dudley had made sure of that. Nevertheless, Harry was determined to find out more about Riddle, so next day...
p. 234.1

nevertheless = despite that (used to connect contrasting ideas)

Definitions:

(1) (nevertheless)
despite that

Based on idea 1 we might not expect idea 2, but this is a way of saying that even though idea 1 was just stated, we still have idea 2. Synonyms include in spite of that, despite that, nevertheless, nonetheless, on the other hand, in contrast and but.
(2) (meaning too rare to warrant focus)