The most common and most likely answer to this crossword clue is the 4 letter word STUB
I've seen this crossword clue in The Times
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More clues leading to the result STUB
- Objections over cigarette end
- Hurt toe, perhaps, first in slippery bath
- Record of payment providing backing for objections
- Butt, or small cask
- Wee bit of pencil, eg, is small, however, returned
- Objections over this residual part of ticket
- Counterfoil of cheque? Objections raised
- Trump’s snipe? Tons penned by junior pressman
- Piece left behind when objections overturned
- Objections about displaying butt
Buddy explains!

The straight part
We know that "Record of payment" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case record of payment = stub.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 STUB mean?
STUB noun- Something blunted, stunted, or cut short, such as stubble or a stump.
- A piece of certain paper items, designed to be torn off and kept for record or identification purposes.
- A placeholder procedure that has the signature of the planned procedure but does not yet implement the intended behavior.
- A procedure that translates requests from external systems into a format suitable for processing and then submits those requests for processing.
- (wikis) A page providing only minimal information and intended for later development.
- The remaining part of the docked tail of a dog
- An unequal first or last interest calculation period, as a part of a financial swap contract
- A log or block of wood.
- A blockhead.
- A pen with a short, blunt nib.
- An old and worn horseshoe nail.
- Stub iron.
- The smallest remainder of a smoked cigarette; a butt.
- To remove most of a tree, bush, or other rooted plant by cutting it close to the ground.
- To remove a plant by pulling it out by the roots.
- To jam, hit, or bump, especially a toe.