The most common and most likely answer to this crossword clue is the 4 letter word BATT
B
A
T
T
More clues leading to the result BATT
Buddy explains!

The straight part
We know that "Layer of quilting" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case layer of quilting = batt.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 BATT mean?
BATT noun- Pieces of fabric or fibre used for stuffing; as for batting or insulation
- (usually in the plural) A shoe.