The most common and most likely answer to this crossword clue is the 6 letter word SERIAL
I've seen this crossword clue in The Guardian
S
E
R
I
A
L
More clues leading to the result SERIAL
- Household gods around to protect one in row
- Nasty sort of killer hides up around Mile End
- Israel involved in a row
- Ongoing story of dosser I allowed inside
- Talk of food crop in The Archers?
- Band of Brothers maybe back from naval air establishment
- Broadcast possible breakfast show
- Set of programmes — something corny on the radio?
- Israel adapted TV show
- Programme that’s put out at breakfast time, in sound only
Buddy explains!

The straight part
We know that "Ongoing story" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case ongoing story = serial.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 SERIAL mean?
SERIAL noun- A work, such as a work of fiction, published in installments, often numbered and without a specified end.
- A publication issued in successive parts, often numbered and with no predetermined end.
- A serial number, esp. one required to activate software.
- To assign a serial number to (especially of aircraft)
- Having to do with or arranged in a series.
- Published or produced in installments.