Middle name distinguishing the sixth US president from the second (6)

I believe the answer is:

quincy

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'second' is the definition.
I don't know anything about this answer so I cannot tell whether it can be defined by this definition.

'middle name distinguishing the sixth us president from' is the wordplay.
I cannot quite understand how this works, but
'name' could be 'cy' and 'cy' is present in the answer.
'from' could be 'in' (I've seen this in other clues) and 'in' is found in the answer.
This explanation may well be incorrect...

'the' is the link.

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I've seen this clue in The Times.

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