is a combination of the 名詞（めいし） (noun) ところ ‘place’, and the 終助詞（しゅうじょし） か. The change from ところ to どころ is a consistent sound change that is seen regularly in sentences that use 所（ところ） negatively.
may be translated as ‘far from’, ‘let alone’ or ‘anything but’. It strongly negates any statement before it, while also emphasizing what comes after it.
may be paired with the 連体形（れんたいけい） (attributive form) of any other word. However, this is not a strict rule, as it can also be seen with the 語幹（ごかん） stem form of な-Adjectives
, and directly attached to nouns.
Far from being sweet, this curry was spicy.
Far from being cold, Hokkaido was hot.
Far from being easy, work yesterday was hectic.
Let alone Chuhai, she doesn't even drink beer.
Sentences that use どころか
must always have a part (B) that emphasizes some type of far more important information (in the speaker's opinion).
As か simply transforms どころ into either a question, or a statement of doubt, the literal translation of どころか
is similar to ‘it’s not even remotely (A)’ as a statement, or ‘do you honestly think it’s (A)!?’, when asking a direct question.
This is not the time to be even remotely that relaxed!
Do you honestly think I would do such a thing? My brother is the only person who would do that.