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Nick Bosa’s family football ties are well chronicled: His dad (John Bosa) and uncle (Eric Kumerow) played for the Miami Dolphins, and his brother Joey (Chargers) and cousin Jake Kumerow (Packers) currently play in the NFL.

Another family connection figures to attract attention during next week’s Super Bowl buildup: Bosa’s great-grandfather was a notorious Chicago mobster who worked closely with Al Capone.

Tony Accardo, a.k.a. Joey Batters, died in 1992, five years before Nick Bosa, who has helped the 49ers return to football’s biggest stage, was even born.

“That’s just not something we talk about,” Cheryl Bosa, Nick’s mom and Accardo’s granddaughter, said by phone Wednesday from her home in Florida. “It has nothing to do with my son playing football.”

Cheryl Bosa struck a pleasant tone in declining to discuss Accardo, in part because she’s accustomed to the questions. And, yes, she realizes Nick Bosa probably will be asked about his great-grandfather during next week’s media crush in Miami.

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“My boys know how to answer those questions,” Cheryl said. “I’m not concerned.”

Accardo, by some accounts, helped plan the 1929 St. Valentine’s Day Massacre, according to a Sports Illustrated story last spring. Accardo became a leader of the organized-crime operation known as the Chicago Outfit after Capone’s conviction for tax evasion in 1931, per the SI piece, and was in full control by the late ’40s.

Accardo’s daughter, Marie, had two children (Cheryl Bosa and Eric Kumerow) with her first husband, Palmer Pyle, a guard with the Colts, Vikings and Raiders in the 1960s. Marie’s second husband, Ernest Kumerow, helped raise Cheryl and her brother Eric.

In 1988, as NFL teams evaluated Eric Kumerow ahead of the draft, his ties to Accardo prompted questions. The Dolphins ultimately took Kumerow with the 16th pick of the first round.

“It’s so silly,” Cheryl Bosa told the Chicago Tribune at the time. “When my brother was drafted, that was a big thing. The teams would interview Eric and they wanted to know if (Accardo) was going to have any impact on changing the game.”

Accardo reportedly earned his nickname by taking two men behind a restaurant and bashing their skulls with a baseball bat. “Boy, this kid is a real Joey Batters,” Capone allegedly said, according to Sports Illustrated.

The SI story also details a robbery at Accardo’s suburban Chicago home in 1978. Accardo, on vacation in California at the time, “seethed over the breach of respect.” Within a year, the story said, 10 men were dead.

Accardo reportedly was involved mostly in gambling operations during his time with the mob. Later in his life, Accardo often watched grandson Eric Kumerow’s high school football games from the stands.

Kumerow didn’t immediately respond to a text message Wednesday, but he once told the Miami Herald of Accardo: “To me, he’s just my grandfather and I love him. He’s a great man, a caring man. I remember him coming to ball games and being with us.”

In 2016, when Nick Bosa was at Ohio State, a TMZ reporter approached him in an airport terminal, asked about Accardo and referred to him as a mob “legend.” Bosa replied, “He’s an undercover legend. He keeps his stuff under the radar.”

And for good reason, apparently.

Ron Kroichick is a San Francisco Chronicle staff writer. Email: rkroichick@sfchronicle.com Twitter: @ronkroichick