A poor penalty by City's an objectionable thing (1,3,5)

'objectionable thing' is the definition.
(term for a bad person or thing)

'a poor penalty by city's' is the wordplay.
I cannot quite understand how this works, but
'a' is within the answer.
'poor' could be 'bad' (similar in meaning) and 'bad' is found in the answer.
'city' could be 'ny' (short for New York) and 'ny' is found in the answer.
The remaining letters 'pen' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).

'an' is the link.

Can you help me to learn more?