“Every time Blue popped up on the screen, my daughter was like, ‘Blue! There’s Blue!’” Marte said. “My daughter just sat up on the edge of her seat like, ‘Yes, this is what I’ve been waiting for.’”

The summer of 2023 saw Blue Ivy, a child born into the spotlight, embrace it and adapt to its demands in real time. Beyoncé’s fans have long had a special connection to her elder daughter, in whom they see the aspirational and the familiar: a child of musical royalty who inspires the same affection and protectiveness as a beloved niece. That attachment was clear during her memorable stage performances and is again on display in the new concert film “Renaissance.”

The movie highlights how, for Beyoncé, the historic tour marked a number of full-circle moments for her: her childhood idol Diana Ross sang “Happy Birthday” to her during one of her L.A. shows; in fashion, song and spirit, she paid tribute to her gay “Uncle Johnny,” who introduced her to house and disco music and helped make costumes for Beyoncé’s former girl group, Destiny’s Child; she even reunited with members of Destiny’s Child when she performed in her hometown of Houston, a reunion she described as “healing.”

But for many Beyoncé fans, the most powerful moment came when Blue Ivy joined her mom onstage during the tour.

Daniel Hall, a 22-year-old social media consultant and Beyoncé fan account owner in Chicago, said he never expected to see Blue Ivy onstage for the Renaissance tour.

“I was in a complete shock, chills over my body,” he said. “For her to be onstage on a tour, where there are primarily fans in the audience that know the gravity of that moment … that was so so fulfilling and so inspiring to me.”

Blue Ivy first danced alongside Beyoncé during her Paris show in May. As Beyoncé recounts in the “Renaissance” documentary, she at first resisted the idea — which was all Blue’s.

“Blue told me she was ready to perform, and I told her ‘no,’” Beyoncé says in the film. “I did not think it was an appropriate place for an 11-year-old, on the stadium stage. All the things I had to go through and the obstacles I had to overcome prepared me — and she hasn’t had that struggle.”

They ended up striking a compromise: If Blue practiced and showed her commitment to performing, Beyoncé would allow her to do one show.

That performance, in front of more than 70,000 people at Le Sade de France, went viral on social media — but to mixed reviews.

Blue appeared visibly nervous in Paris, her head sometimes swiveling to look at her mother or dance captain Amari Marshall. Some criticized her dancing: the moves weren’t crisp enough; she missed steps; they knew other 11-year-olds who could dance better.

Blue herself got wind of the criticism from a friend, according to Beyoncé. Her daughter felt like she had to prove herself. So she kept performing at various stops along the “Renaissance” tour, getting demonstrably better with each performance.

“It was magical,” Beyoncé says. “Her confidence just grew and grew. It was a beautiful thing for her.”

By the time Adrienne Carter, an insurance underwriter, saw the “Renaissance” tour in Charlotte this summer, Blue Ivy’s appearance was one of the most anticipated parts of the show. In the moments before Blue’s appearance, Carter noticed everyone around her craning their head, trying to catch a glimpse of Blue Ivy rising up from beneath the stage.

The timing is also meaningful. She appears during “My Power,” a battle-cry of a song in which Beyoncé calls out her “bloodline, on the front line,” as well as “Black Parade,” an anthem of Black pride.

When Blue’s upheld fist emerged, the crowd was ecstatic.

“If I would have went to a show were Blue Ivy did not come out, I would honestly be disappointed,” Carter said. “To me, it was a defining moment of the tour.”

Carter can remember when Beyoncé announced her pregnancy with Blue Ivy onstage at the 2011 MTV Video Music Awards, when the singer pulled back her sequined jacket at the end of “Love on Top” to reveal a baby bump.

Seeing Blue Ivy grow up in the public eye has made her feel familiar, even if much of her life is aspirational: “She’s like my faraway niece that I will never meet,” Carter said.

The daughter of a once-in-a-generation performer and Jay-Z, one of the greatest rappers of all time, Blue Ivy has been the subject of adoration and scrutiny since she was an infant.

Beyoncé — and by extension, Blue Ivy — keeps many details of her personal life private. But their public moments have offered a window into their dynamic as mother and daughter.

During a rehearsal for the Grammy Awards in 2014, Blue was given a microphone to talk to her mom onstage. Beyoncé instantly melted as she heard the 2-year-old say “Hi mommy” over and over again. On the red — in fact, blue — carpet at the London premiere of the movie, Beyoncé stepped away from the flashing cameras for her mom duties: “Wait a minute — she’s cold,” she told the photographers.

Fans have long joked that Blue Ivy acts as Beyoncé’s manager, ever since she motioned for her parents to stop clapping at the 2018 Grammys. The running gag is alive and well, as the movie shows video proof that Blue’s mom kept “Diva” in the tour set thanks to the 11-year-old’s insistence.

These moments help ground Beyoncé’s image — Beyhive members say they are reminded of their own families when witnessing these moments: mothers who coached their daughters in dancing; kids who relished performing because of the pride it brought their parents.

But Blue Ivy has also received an undue amount of criticism because of who her mother is, fans say, recalling criticisms of Blue’s natural hair or facial features. Jay-Z alluded to this disparagement in his own retelling of Blue’s “Renaissance” tour story, in a CBS interview with Gayle King that aired in November.

“I still get goose bumps just seeing her walk onstage — just because Blue’s been born into this world that she didn’t ask [for]. She’s been born into a life she didn’t ask for,” he said. “So for her, to be on that stage and reclaim her power, and the song is called ‘My Power,’ you can’t write a better script.”

Victoria Harvey, a nonprofit development director who lives in Washington, D.C., said she didn’t consider herself the biggest fan of Beyoncé but was converted after seeing her perform — “I’ve never seen anything like that before.” The moment with Blue Ivy was especially powerful.

She felt an enormous amount of pride in seeing Blue Ivy embody such confidence and poise: Here was a little Black girl, whom she once saw as a niece or little cousin, now a “young lady” coming into her own.

It brought her to tears, Harvey said, to think of how Blue Ivy seemed to be stepping into a family legacy in real time. “I wish that opportunity for so many other Black young people,” Harvey said.

“I’m excited to see her grow up and see what she becomes on her own.”