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As one of the most private men to ever play baseball in New York, Derek Jeter probably never expected to make enemies of his neighbors.

But on Davis Island in Tampa, Fla. — where the legendary Yankee shortstop retreated full time after his 2014 retirement — locals know Jeter’s 30,875-square-foot manse as the place where a menace lives.

His name is Kane.

“[Jeter’s] got this Italian mastiff, and it’s vicious. When he first got it, it was a cute little puppy, but it became controversial on the block,” says one neighbor of the 1 ½-year-old pooch, gifted to Jeter by model fiancée Hannah Davis for Christmas in 2014. “All of the dogs are afraid of him. He was outside barking all of the time. It wasn’t a normal bark. It was a bark you could hear blocks away.”

Last November, Jeter wrote on his Players’ Tribune Web site that he was “previously scared of dogs” and that “discipline is proving difficult” with the 100-plus-pound Kane.

Lately though, neighbors haven’t seen as much of the mastiff, and they suspect Jeter, 41, is keeping him indoors more. No surprise for a guy who’s never been willing to lift the curtain on his private life.

When he was on the Yankees, Jeter was one of the most famous athletes on the planet, to the point that he couldn’t walk down the street without being mobbed. Now, at 41, he can do whatever he wants —and that means dabbling in a little of everything as he tries to sort out what suits him best.

Even as Jeter remains mostly behind closed doors when he’s off-duty, retirement has brought out a surprising second side of the former Yankee — the smiling, elbows-rubbing pitchman.

He’s zeroed in on becoming a media and publishing mogul, with the Players’ Tribune as well as a book imprint. He’s also very involved in his 20-year-old Turn 2 Foundation, which works to encourage leadership skills in kids.

Unlikely as it sounds, Jeter’s even an investor in Luvo, a company that makes low-sodium, pre-prepared meals — he’s even hawked the frozen food on the streets of Manhattan as a publicity stunt.

The five-time World Series champ is also popping up on red carpets and talk shows — things that never happened while he was in pinstripes.

What always made Jeter great was his laser-like focus. For most of his life, it was on baseball. Now, insiders chalk up his more-approachable persona to the simple fact that he has a new focus: selling himself.

Earlier this month, Jeter faced some 40 literary agents at the Paley Center in Midtown.

The ex-Yankee was there to pitch himself as a serious player in the book industry, wooing said agents to work with his Simon & Schuster imprint, Jeter Publishing, launched in 2013.

Recent releases include the kids’ book “Night at the Stadium,” which is described in press materials as a combination of “Field of Dreams,” “Alice in Wonderland” and “A Night at the Museum.”

But it hasn’t all been home runs — Jeter revealed to the agents that his imprint had gone after comedian Tracy Morgan’s memoir but missed.

“[Jeter] talked about being very involved in the acquisitions process,” says agent Jennifer Keene, who attended the meeting. “[He and his partners] stressed that Derek’s name is on the imprint doesn’t just mean [authors] are signing up — and they aren’t just throwing money at people. There is a sound business sense there.”

Sources say Jeter is also hands-on with the Players’ Tribune, his Web site that features profiles told from the athletes’ perspective. Last November, the Tribune had its first big scoop — Kobe Bryant’s retirement announcement, which crashed the site. And in March, Yankee CC Sabathia penned an essay detailing his alcohol addiction and rehab.

Several people involved with the site say Jeter stops in to the Chelsea office when he is in town and keeps in touch via video conference.

Explaining his inspiration for the site, Jeter wrote, “I do think fans deserve more than ‘No comments’ or ‘I don’t knows.’”

Again, a telling remark for a man who’s always been standoffish with the press.

As the captain of the Yankees, Jeter could come off as controlling to the point of being cold. But Keene says that at the publishing event, Jeter “was mixing and mingling. It wasn’t one of those situations where the celebrity comes out at the last minute.”

Indeed, Jeter in retirement seems more relaxed, warmer. The night before his literary event, he attended the fashion-world prom that is the Met Gala, on the arm of Sports Illustrated Swimsuit Issue cover girl Davis for a second year.

“In a room full of people who are insanely famous, Jeter is someone everyone is always excited to meet,” says a source close to gala organizers.

“It’s not that he didn’t want to go the Met Ball or do media [before retiring]. With his baseball schedule, he was never able to do it,” says another source.

During that same whirlwind New York trip, he dropped by “Late Night With Seth Meyers” to promote his books and showcase his humorous side, by trash-talking Red Sox faithfuls.

“[When they come up to me,] they always say, ‘I’m sorry, but I’m a Boston fan,’ ” Jeter told Meyers, who is a devotee of the Beantown ball club. “I don’t care if you’re a Boston fan. We’re not at the stadium. Just don’t yell at me in restaurants. Boston fans have softened up since you guys won [three recent World Series]. It pains me to say . . . I am not happy you won, but you treat me a lot better.”

Among Jeter’s Davis Island neighbors are former Tampa Bay Buccaneer Brad Culpepper, who lives next door, and Tampa Bay Lightning player Ryan Callahan (formerly of the New York Rangers). But it’s unlikely they’ve hung out, as Jeter hasn’t been home much since quitting baseball.

During his season-long retirement tour, the Yankees gave Jeter a 10-day trip to Tuscany, Italy, the Oakland A’s gifted him a trip to a Napa Valley resort, and Toronto delivered a stay in the Canadian Rockies.

“He’s been a globe-trotter,” says a baseball source. “A lot of teams offered trips, and he made good on all of them.”

When he is in his new hometown, spottings are rare.

“He is very much under the radar. Unlike most athletes in Tampa, he’s not visible on the club scene, the charity scene or even at the gas station,” says Amy Scherzer, society columnist for the Tampa Bay Times. “The most frequent sightings [are] at the Avila country club,” where he plays golf and where the priciest menu item is the $38 strip steak with soup or salad.

Much of his home time is no doubt spent nesting with Davis, his fiancée.

Once a notorious bachelor who dated celebs like Mariah Carey and Minka Kelly, Jeter popped the question in October with a diamond estimated to be between four and six carats.

Details of the wedding are predictably being kept under wraps, but Davis revealed at Fashion Week that she will be wearing Vera Wang for the big day.

While the guest list is a mystery, sources say Jeter has remained close to former teammate Jorge Posada. A possible wedding locale is Jeter and Davis’ sprawling compound in St. Thomas, Virgin Islands, where Davis grew up.

One thing Jeter didn’t do much of right after retiring? Watch baseball.

“My first year in retirement, I needed to get away from it, so I didn’t watch,” he told Meyers.

He only visited Yankee Stadium twice last season, to honor Bernie Williams and Andy Pettitte during their respective number-retirement ceremonies.

But, he told Meyers, “I’m starting to watch [baseball] a little bit more, because ultimately I have ownership aspirations.”

In December 2014, The Post reported that Jeter was interested in buying the Miami Marlins. But mercurial Marlins owner Jeffrey Loria shot down the report this week, telling The Post, “None of this is true.”

Still, whispers persist around Jeter’s new hometown that he may chip in to buy the beleaguered Tampa Bay Rays, a team that has struggled with attendance.

“There are rumors that Derek will become a partner with current owner Stuart Sternberg and help him build a new stadium,” says Scherzer.

Jeter fueled speculation in March when he showed up in Havana to watch the Rays play an exhibition game against the Cuban national team.

And New Yorkers are hoping for a Jeter homecoming on Aug. 13, when it’s speculated he’ll return to Yankee Stadium to commemorate the 20th anniversary of the 1996 World Series win.

As a source close to Jeter puts it: “If you go to work for 20 years, are you going to visit your old office frequently? I don’t think so.”