RDreher
I found a historic maps which shows this as the home of H.A. "Blakelee" lol.

https://historicmapworks.com/Map/US/1498/Coventry++Columbus+Town++Coventry+Town/Chenango+County+1875/New+York/

The discrepancy in spelling is very annoying, but it likely has to do with the fact that historically spelling was way more fast and loose. "Blackesley Corner" appears far more often in google searches than "Blakesley Corner," so it's likely that this place has been spelled wrong so long that it's kind of stuck, but all these mentions are likely just reading from maps, not from any official records or government sources. However, hamlets do not get much official recognition in NY, not like towns or villages. Blakesley seems more correct to me, but as of now I have about equal grounds for both. The local historical society, which should know the region well, says it's Blackesley, but the state government says it's Blakesley.