A cloud of discontent that always seems to be menacing Staten Island, where people are accustomed to feeling ill used by the rest of New York City, is darker than usual these days.  Friday was the 50th anniversary of the opening of the Verrazano-Narrows Bridge, the structure that linked the island to Brooklyn and, in doing so — according to some Staten Islanders, anyway — ruined everything. And if that was not bad enough, the Metropolitan Transportation Authority was, once again, threatening to raise the cash toll on the bridge by $1, to $16.  “They were supposed to pay it off 20 years ago,” said Liz DeMartino, who was born the day the bridge was lit for the first time, in 1964. “And we’re still paying.”  Mention the ever-increasing Verrazano toll to Staten Islanders, and one is likely to hear some version of the following: Crossing the bridge was supposed to be free once it was paid for. Yes, they read this in the paper somewhere. Or someone told that to them once. Or they do not remember how they heard, exactly, but everybody knows about it.  Fifty years after the suspension bridge brought a flurry of migrants and construction to the island, nobody can seem to find any proof that any such promise was made. Yet despite repeated debunking, the belief has endured: part cherished urban myth, part rallying cry, vigorously invoked every time the E-ZPass statement arrives or the toll is going up.  “I’ve heard it discussed by a lot of reputable people,” said the borough historian, Thomas W. Matteo, who watched the bridge’s construction as a boy growing up in Dyker Beach, Brooklyn, and then joined the masses moving to Staten Island after it was built. “But as far as a document, a smoking gun, I never recall seeing one.”  Nor does the transit authority, which felt compelled to burrow into its files a few years ago looking for records on the subject, only to come up empty-handed.  And not The Staten Island Advance, which has published at least three articles in the past five years in an effort to convince its readers that the toll would never disappear. The newspaper tried, and failed, to put the story to rest once and for all in 2009, when it scoured its archives from before and after the bridge’s opening and found no mentions of a toll-free crossing.  “Believe whatever you want,” concludes a February article, with the air of someone washing his hands of the whole business, “but we insist you’ll be wrong.”  Nine months later, deluged once again by skeptical online commenters, The Advance published yet another denial.  Still, the borough still reaches for the old grievance as an invigorating tonic.  “They have a lot of nerve charging Staten Islanders,” Michelle Mendez-Rudman of Dongan Hills said as she and her husband left Bagels N’ Buns on Victory Boulevard on Wednesday afternoon. “Where’s this money going? Who’s pocketing it?”  There was, it is true, a bridge that was supposed to be free after the bonds used to pay for it were retired: the Triborough Bridge (now the Robert F. Kennedy Bridge), which connects Manhattan, Queens and the Bronx, built a quarter-century before the Verrazano. But, as Robert A. Caro recounted in his book “The Power Broker,” the Triborough proved too much of a coin cow for Robert Moses, the master planner who midwifed both structures. He had the law amended to let the Triborough Bridge Authority stay in business, and collect tolls indefinitely, by issuing new bonds.  By the time the Verrazano rose, however, it seemed clear that neither bridge would ever be free. According to The Advance, Mr. Moses shot down repeated pleas from a Staten Island politician to reduce fees for the island’s residents. His Triborough Bridge and Tunnel Authority imposed a 50-cent toll. (Mr. Matteo recalled that some drivers used Mexican pesos, which were about the right size to fool the coin-collecting bins.)  For Staten Islanders, it was just another on a long list of indignities. “The way it went in those days was, if you had something that was objectionable to the communities, send it over to Staten Island,” said Guy V. Molinari, a Republican who served as borough president and as a member of Congress.  He attributed the no-toll myth to politicians trying to make the bridge more palatable. “These would be the kind of off-the-cuff things that would be said to overcome community opposition,” he said.  When the Triborough agency was subsumed into the new Metropolitan Transportation Authority, the bridges continued to charge tolls. They have helped prop up buses, subways and commuter railroads ever since.  That is little consolation to car-dependent Staten Islanders, many of whom did not even want the bridge in the first place, fearing — rightly, as it turned out — that their borough’s quiet would be overrun by newcomers, its rolling farmland bulldozed for new buildings.  “We definitely were lied to,” said Ray DeVito, a Consolidated Edison worker who recalled the years before the bridge as an idyll. “Why should we subsidize a train station we don’t even use?”  As to the accusation of lying, the authority is accustomed to explaining that its archives hold no record of any no-toll agreement.  “It comes up all the time,” said Judie Glave, a spokeswoman, with a hint of exasperation. “And we have no idea where it came from.”  At least Staten Islanders can get a discount on the toll, offered as a salve to incensed local residents by Gov. Andrew M. Cuomo and his father, former Gov. Mario M. Cuomo. In 1983, the elder Mr. Cuomo signed a law lowering the charge for island residents to $1 each way, from $1.25; this year, his son, a fellow Democrat, agreed to a reduction in the toll, now charged only in the westbound lanes, to $5.50 for Staten Island residents with an E-ZPass, from $6.  The authority, though, is threatening to raise that rate by 24 cents, part of a range of toll and fare increases under consideration. Citing the proposals, several Staten Island elected officials boycotted the celebration on Friday of the 50th anniversary, which included a 50-shot cannon salute and a fireboat water display.  There is no discount for residents on the Brooklyn side of the Verrazano, where hundreds of homes were demolished and thousands of people uprooted to make way for it, and where the myth of the free bridge is believed with equal fervor.  All of which has left Councilman Vincent J. Gentile, Democrat of Bay Ridge, Brooklyn, seeking to do some debunking of his own. He wishes to make it known that, when it comes to the disrespect that the Verrazano has handed out for 50 years, no neighborhood has been more disrespected than his.  “I’m just upset about this whole celebration,” he said of the anniversary ceremonies. “It’s Staten Island-centric. A bridge has two sides, you know?”  A version of this article appears in print on November 22, 2014, on page A16 of the New York edition with the headline: Linked by a Bridge, and a Myth. Order Reprints| Today's Paper|Subscribe
Ever since the Verrazano-Narrows Bridge opened on Nov. 21, 1964, Staten Islanders and Brooklynites have maintained that they were promised a toll-free bridge, but no proof exists to back that claim.