The most common and most likely answer to this crossword clue is the 6 letter word BAWBEE
B
A
W
B
E
E
More clues leading to the result BAWBEE
Buddy explains!

The straight part
We know that "Halfpenny" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case halfpenny = bawbee.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 BAWBEE mean?
BAWBEE noun- A coin originally worth six pennies Scots, and later three; held equivalent to an English halfpenny.
- A copper; a small amount of money.