Both Uses

nevertheless
in
The Horse and His Boy
(Edited)

Moreover he is at least sixty years old and has a hump on his back and his face resembles that of an ape. Nevertheless my father, because of the wealth and power of this Ahoshta, and being persuaded by his wife, sent messengers offering me in marriage,
Chpt 3 *

nevertheless = despite that (used to connect contrasting ideas)
"Your royal Highness needs not to be told," said King Lune, "that by the law of nations as well as by all reasons of prudent policy, we have as good right to your head as ever one mortal man had against another. Nevertheless, in consideration of your youth and the ill nurture, devoid of all gentleness and courtesy, which you have doubtless had in the land of slaves and tyrants, we are disposed to set you free, unharmed, on these conditions: ..."
Chpt 15

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)