The most common and most likely answer to this crossword clue is the 6 letter word EYELID
I've seen this crossword clue in Financial Times
E
Y
E
L
I
D
More clues leading to the result EYELID
- It’s a blinking requirement
- Cry endlessly in religious festival — one dropped to sleep?
- Shutter protecting lens
- Flap causing momentary lack of vision
- Lampshade?
- Dream may get one flapping a bit
- . Returning crocodile yet to eat part of body
- Palpebra hat reportedly made by the Apple Corporation?
- Examine Latin papers – it’s beneficial to pupil
- Papers alongside fish soaking up last of oily batter
Buddy explains!

The straight part
We know that "batter" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case batter = eyelid.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 EYELID mean?
EYELID noun- A thin skin membrane that covers and moves over an eye.