A list dutifully worked on (4)

I believe the answer is:

rota

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'a list' is the definition.
(rota is a kind of list)

I can't explain the rest of the clue.

(Other definitions for rota that I've seen before include "List assigning turns of duty" , "List of duties to be done, or people to do them" , "Duty roster" , "Task list, roster" , "Roll call or roster" .)

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