Two long-shots, Curtis Sliwa, the founder of the Guardian Angels, and Fernando Mateo, a restaurateur, are in a heated fight to be their party’s nominee.The two Republicans running for mayor of New York City used to be friends. They are both first-time candidates, long shots for the job and tabloid fixtures who perk up when they see a news camera.And now they are at war.At an in-person debate this spring, Fernando Mateo, a restaurateur, threatened his old friend Curtis Sliwa, the founder of the Guardian Angels, for what he said were attacks on his character and warned that he had damaging information about his opponent.“I have enough dirt to cover your body 18 feet over,” Mr. Mateo said.Mr. Sliwa had called Mr. Mateo a “de Blasio Republican” and accused him of breaking the law in his fund-raising efforts for Mayor Bill de Blasio, a Democrat.“Shame on you,” Mr. Mateo responded, calling the allegations “fake news.”They will meet again on Wednesday, this time virtually, at the first official Republican debate, which will be broadcast on NY1.The Democratic primary for mayor has grown increasingly negative, with Andrew Yang, the former presidential hopeful, and Eric Adams, the Brooklyn borough president, calling for investigations into each other’s fund-raising. But they have nothing on the Republicans, who despite their slim chance of winning City Hall seem intent on destroying each other in a scorched-earth primary campaign.It can be easy to forget that not that long ago, New York City elected back-to-back Republican mayors — Rudolph W. Giuliani and Michael R. Bloomberg — and that the Republican Party held its own in large sections of the city outside Manhattan. Today the party’s political power has weakened to the point where the Democratic primary, not the general election, will almost certainly decide who will be the next mayor.But the Republicans are still battling each other to become the face of the party. Mr. Sliwa, whose menacing crime-fighting squads made him a celebrity in the 1980s, is hoping that his public profile and law-and-order message, coming at a time of rising crime, can give him the edge both in the June 22 Republican primary and in the general election in November.Mr. Sliwa rode the subway for 24 hours straight last week, wearing his signature red beret and calling for 5,000 more police officers to stem violence in the system. Instead of defunding the police, he said, he wants to “re-fund the police.”In the 168th Street station in Manhattan, he greeted two officers.“You might be our savior,” one officer told him.Mr. Sliwa, who joined the Republican Party only a year ago, has brought a showman’s zest to the race. He was trailed by cameras as he brought a cake with a giant meatball on top of it to Gracie Mansion to taunt Mr. de Blasio on his 60th birthday — he was protesting the city’s decision to remove Columbus Day from the school calendar — and he hosted a mask-burning ceremony while a disco band sang “Burn Baby Burn.”Mr. Mateo, who was born in the Dominican Republic, is focusing on his story as an immigrant. He wants to become the city’s first Hispanic mayor and has called for overturning bail reform and keeping the jail at Rikers Island open.Republican leaders are split between the candidates. The Manhattan, Queens and Bronx parties endorsed Mr. Mateo. The Staten Island and Brooklyn parties backed Mr. Sliwa.Mr. Mateo is leading in fund-raising: He has raised about $520,000 and says he will qualify for public matching funds soon. (A candidate must raise at least $250,000 in contributions of $250 or less from at least 1,000 city residents to qualify.). Mr. Sliwa has raised about $315,000.There is little polling to know where the candidates stand. Mr. Sliwa was leading among older registered Republican voters with 40 percent, compared to 6 percent for Mr. Mateo, in an AARP-Siena poll in April. But about 44 percent of voters were undecided.Mr. Sliwa rode the subways for 24 hours recently.Andrew Seng for The New York TimesBoth face an uphill battle in a city where Democrats outnumber Republicans by more than six to one. Republicans have lost influence in the city since Mr. Giuliani was elected in 1993 and Mr. Bloomberg in 2001. Today the party has only a handful of elected officials in the city, with most from Staten Island, including James S. Oddo, the borough president, and Representative Nicole Malliotakis.Even Joseph J. Lhota, the Republican candidate for mayor who lost to Mr. de Blasio in 2013, left the party. He is supporting Kathryn Garcia, the city’s former sanitation commissioner and a Democrat, for mayor.Mr. de Blasio, a Democrat who is in his second term, said this week that the Republicans had no chance of succeeding him.“It’s a side show honestly,” he said. “They don’t have a snowball’s chance in hell of winning a general election, so God bless them.”But some Republicans see an opportunity. Joseph Borelli, a Republican city councilman from Staten Island, said the atmosphere in the city resembles the early 1990s, when Mr. Giuliani won City Hall amid rising crime and concerns over quality of life.“Just look at how the Democrats made a 180-degree turn on policing the minute there was a horrific shooting in Times Square,” he said. “They went from defund the police to ‘of course the police are part of the solution’ in less time than it takes to drive down Broadway.”Mr. Sliwa, 67, founded the Guardian Angels in 1979 after working as a night manager at a McDonald’s in the Bronx. The Angels’ patrols grabbed headlines, though Mr. Sliwa later confessed that they faked crimes for publicity..css-1xzcza9{list-style-type:disc;padding-inline-start:1em;}.css-3btd0c{font-family:nyt-franklin,helvetica,arial,sans-serif;font-size:1rem;line-height:1.375rem;color:#333;margin-bottom:0.78125rem;}@media (min-width:740px){.css-3btd0c{font-size:1.0625rem;line-height:1.5rem;margin-bottom:0.9375rem;}}.css-3btd0c strong{font-weight:600;}.css-3btd0c em{font-style:italic;}.css-w739ur{margin:0 auto 5px;font-family:nyt-franklin,helvetica,arial,sans-serif;font-weight:700;font-size:1.125rem;line-height:1.3125rem;color:#121212;}#NYT_BELOW_MAIN_CONTENT_REGION .css-w739ur{font-family:nyt-cheltenham,georgia,’times new roman’,times,serif;font-weight:700;font-size:1.375rem;line-height:1.625rem;}@media (min-width:740px){#NYT_BELOW_MAIN_CONTENT_REGION .css-w739ur{font-size:1.6875rem;line-height:1.875rem;}}@media (min-width:740px){.css-w739ur{font-size:1.25rem;line-height:1.4375rem;}}.css-9s9ecg{margin-bottom:15px;}.css-1jiwgt1{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;-webkit-box-pack:justify;-webkit-justify-content:space-between;-ms-flex-pack:justify;justify-content:space-between;margin-bottom:1.25rem;}.css-8o2i8v{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;-webkit-flex-direction:column;-ms-flex-direction:column;flex-direction:column;-webkit-align-self:flex-end;-ms-flex-item-align:end;align-self:flex-end;}.css-8o2i8v p{margin-bottom:0;}.css-12vbvwq{background-color:white;border:1px solid #e2e2e2;width:calc(100% – 40px);max-width:600px;margin:1.5rem auto 1.9rem;padding:15px;box-sizing:border-box;}@media (min-width:740px){.css-12vbvwq{padding:20px;width:100%;}}.css-12vbvwq:focus{outline:1px solid #e2e2e2;}#NYT_BELOW_MAIN_CONTENT_REGION .css-12vbvwq{border:none;padding:10px 0 0;border-top:2px solid #121212;}.css-12vbvwq[data-truncated] .css-rdoyk0{-webkit-transform:rotate(0deg);-ms-transform:rotate(0deg);transform:rotate(0deg);}.css-12vbvwq[data-truncated] .css-eb027h{max-height:300px;overflow:hidden;-webkit-transition:none;transition:none;}.css-12vbvwq[data-truncated] .css-5gimkt:after{content:’See more’;}.css-12vbvwq[data-truncated] .css-6mllg9{opacity:1;}.css-1rh1sk1{margin:0 auto;overflow:hidden;}.css-1rh1sk1 strong{font-weight:700;}.css-1rh1sk1 em{font-style:italic;}.css-1rh1sk1 a{color:#326891;-webkit-text-decoration:underline;text-decoration:underline;text-underline-offset:1px;-webkit-text-decoration-thickness:1px;text-decoration-thickness:1px;-webkit-text-decoration-color:#ccd9e3;text-decoration-color:#ccd9e3;}.css-1rh1sk1 a:visited{color:#333;-webkit-text-decoration-color:#ccc;text-decoration-color:#ccc;}.css-1rh1sk1 a:hover{-webkit-text-decoration:none;text-decoration:none;}Mr. Sliwa was shot five times in the 1990s, arrested at least 77 times, testified at the federal trial for John A. Gotti, a Mafia boss, and married four times. He had two children with Melinda Katz, now the Queens district attorney, before marrying his current wife, Nancy, who is a member of the Guardian Angels.He was a radio host and led the Reform Party of New York State before officially becoming a Republican last year. He has received criticism for many of his public comments over the years, including saying in 2015 that he wanted to have sex with the speaker of the City Council, Melissa Mark-Viverito.His main campaign issue, beyond public safety, is property tax reform — a pressing issue for many homeowners outside Manhattan. Mr. Sliwa said he also wants voters to know that he has a compassionate side, rescuing cats that he keeps in his home on the Upper West Side.“I live in a 320-square-foot studio apartment with one toilet and 15 rescue cats,” he said in an interview. “There’s a lot of litter changing.”Mr. Mateo, 63, moved to New York City as a child, dropped out of school at 14 and started a carpet business. He later got involved in civic issues, creating groups to advocate for livery drivers and bodega owners, and he became a major political donor.Mr. Mateo advocated for livery drivers and bodega owners.Michael M. Santiago/Getty ImagesHe is perhaps best known for his “Toys for Guns” program in the 1990s, when he offered toy store gift certificates in exchange for guns. It got 3,000 guns off New York streets, was replicated in other cities and made him a hero in the national news media.In 2018, he faced negative headlines over his waterfront restaurant La Marina, in the Inwood neighborhood in Manhattan, where there were complaints about drugs and noise, and he was linked to a scandal involving fund-raising by Mr. de Blasio.Mr. Mateo now runs another restaurant, Zona de Cuba in the Bronx, and says he works there in the evenings after long days on the campaign trail — a point of pride.“I’m making a living or I’m campaigning — I’m the only candidate that does that,” he said in an interview. “I know what it’s like to meet payroll.”His main proposal is a teen jobs program, which he calls “Alpha Track,” to keep students out of trouble.But for all of his positive talk about his life story and giving young New Yorkers the same opportunities, he is also taking aim at Mr. Sliwa, who has said he did not vote for President Donald J. Trump in 2020.“I’m the only true Republican in this race,” Mr. Mateo said. “I voted for Trump twice.”He said their feud began when he entered the race, and Mr. Sliwa began to attack him.“I thought that Curtis was my friend,” he said. “I carpeted his first apartment.” More