American state capital is NY? Hence managing to smuggle drug (8)

I believe the answer is:

cheyenne

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'american' is the definition.
(I have seen 'Native American' mean 'cheyenne' so perhaps 'american' could also mean 'cheyenne')

I don't understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for cheyenne that I've seen before include "US city" , "native language" , "US state capital" , "Native American of Montana or Oklahoma" , "tongue" .)

I've seen this clue in The Hindu.

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