The most common and most likely answer to this crossword clue is the 4 letter word MURK
M
U
R
K
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The straight part
We know that "fog" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fog = murk.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does MURK mean?
MURK adjective- Dark, murky
- Darkness, or a dark or gloomy environment.
- To make murky or be murky; to cloud or obscure, or to be clouded or obscured.
- To murder or seriously injure.