The most common and most likely answer to this crossword clue is the 3 letter word VOW
V
O
W
More clues leading to the result VOW
Buddy explains!

The straight part
We know that "Assertion" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case assertion = vow.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 VOW mean?
VOW noun- A solemn promise to perform some act, or behave in a specified manner, especially a promise to live and act in accordance with the rules of a religious order.
- A declaration or assertion.
- A votive offering.
- To make a vow; to promise.
- To make a vow regarding (something).
- To declare publicly that one has made a vow, usually to show one's determination or to announce an act of retaliation.