But the owner, Red Brennen, a retired marine contractor, has had just about enough of paying taxes for a place he can no longer use now that he is out of the barge salvaging business and lives in Florida. He put his land up for sale in 2009 for $300,000; he had some nibbles, but no real bites. Now he is putting the property up for auction, on Sunday, through Alex Lyon & Son. The land — most recently valued by the city at $426,000, according to a spokesman for the Finance Department — could go to the highest bidder, unless Mr. Brennen rejects the offer.

“The only thing I’m going to own after I sell Rat Island and my real estate is my E-ZPass,” said Mr. Brennen, who pays nearly $1,500 a year on the island and is also auctioning off property on City Island. “New York City and State won’t be able to hurt me anymore.”

Originally part of Thomas Pell’s land purchase from the Siwanoy Indians in 1654, the island did not become part of the city until the 1880s when it began acquiring land for Pelham Bay Park, said Barbara Dolensek, vice president of the City Island Historical Society.

Much of its history is lost and shrouded in folklore; the name is said to relate to prisoners, called rats, escaping from Hart Island, swimming with cardboard boxes over their heads to look like bobbing trash, but it is not clear if that is true. Legend also holds that the island was used as a so-called pest house in the 19th century to quarantine people infected with yellow fever, but Bronx and City Island historians have said that was unlikely because the city already had a quarantine hospital on Hart Island, now known as the site of the city’s potters field.

Rat Island, said to have served as an artists and writers colony, has supported at least one cottage; the remnants of a stone foundation still sit on a peak. Within its perimeter on Thursday was a lone rubber glove and a single green-and-gray Aldo men’s size 42 deck shoe with socks scrunched inside. Whether they had been discarded there or washed ashore was not entirely clear.