The most common and most likely answer to this crossword clue is the 4 plus 1 plus 5 plus 3 letter word WELL I NEVER DID
I've seen this crossword clue in The Guardian
W
E
L
L
I
N
E
V
E
R
D
I
D
More clues leading to the result WELL I NEVER DID
Buddy explains!
The straight part
We know that "My" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case my = well i never did.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.