Zak DeOssie remembers waiting on a corner in North Andover, Massachusetts, for the school bus to come on that Monday morning and bring him to another day of first grade. His buddy from next door, Sean Phelan, met him there as usual.

“I said: ‘Hey, my dad won the Super Bowl last night,’ ” DeOssie recalled of the conversation between 6-year-olds. “And he said: ‘Oh. Cool. Want to go climb this tree?’ That was the extent of the celebration outside of the house.”

It’s every football player’s dream to play in the NFL and win a Super Bowl. Not everyone gets to experience that. But there are three Giants players this season who grew up with a father who accomplished the feat and reached the pinnacle of the sport before them. As their quest for a Super Bowl begins this season, their experiences with that legacy vary widely, but there is a common denominator of wanting to meet — or eclipse — the achievement.

“It’s obviously the ultimate goal for me personally, for my family, for this organization and for this team,” linebacker Devon Kennard said. “To be able to put a Lombardi Trophy up in Giants Hall and in my own home one day would be awesome.”

Unlike DeOssie, who was largely unfazed by his father Steve’s role as a member of the Giants’ Super Bowl XXV team (“It was just what my dad did and I didn’t know the scope of it all,” he said), Kennard always was proud that his father, Derek Kennard, had won the big game as an offensive lineman for the Cowboys. He was the starting center in Super Bowl XXX.

“The thing that fascinated me was the Super Bowl trophy,” Kennard said of a replica of the Lombardi Trophy each of the players received. “It was in our basement. That’s where I would play all the time and he had it there in a glass case and I just remember every time I was in the basement, at some point I would look at it and think about it.”

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And when friends came over, Kennard was quick to point it out, too. Not that he always needed to.

“It kind of draws its own attention,” he said.

DeOssie had a replica of the trophy as well. He kept his in his bedroom.

“My friends would all take a look at it,” he said. “As I got older, it got cooler and cooler. Once football took off for me around the high school level, it kind of clicked that it was a pretty big deal that my old man made it into the NFL and won a Super Bowl.”

Giants rookie Sterling Shepard’s father, Derrick, passed away when Sterling was 6. He was a member of the 1987 Redskins team that won Super Bowl XXII, but unlike Kennard and DeOssie, he doesn’t have any bling-like reminders of the experience.

Derrick Sheppard was one of the replacement players for Washington during the three games in which NFL players were on strike that season. He remained with the team after the strike was settled — one of the few who parlayed the experience into an NFL career — but never received a Super Bowl ring for his part in the season. Many point to the replacement players going 3-0 during the strike — including a win over the Cowboys, who had several stars such as Tony Dorsett and Randy White cross the picket line to play — as a major element of the championship run. Still, no keepsake for Shepard.

“We really never knew the reason and he never asked,” Cheri Shepard, Sterling’s mother and widow of Derrick, told Newsday of not receiving a ring from Washington. “He was so happy to be on the team, he was reluctant to ask any questions regarding the ring.”

Sterling Shepard said he has a much deeper relationship with his father’s national championship ring, which he won with Oklahoma in 1985.

“My mom gave it to me after I graduated from college in December,” he said.

Now his quest is to become the second person in his family to win a Super Bowl, but the first to get a ring.

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“That’d be a cool deal,” he said.

While most players these days are focused on getting “the ring,” Kennard said he was less impressed by his father’s keepsake jewelry than that replica trophy.

“The only thing I remember about the ring is my dad has huge fingers, so I would break it out sometimes and show friends and we would always joke [about the size],” Kennard said. “When I was young, I could almost fit it on my wrist, it was so big.”

Kennard and Shepard would like nothing more than to match their fathers’ Super Bowl traditions with the Giants this season. Such a father-son connection would be unimaginably poignant, as DeOssie already knows.

“Obviously, you’ve reached the pinnacle of your career and that’s nice, but being able to share that with your father is an inexplicable feeling,” DeOssie said of winning Super Bowl XLII as a Giants rookie. “He was the first one to grab me on the field outside of my teammates and we both just absolutely lost it, crying and hugging.”

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DeOssie, of course, won another Super Bowl four years later with the Giants.

“When we won the second one, after a few tears, I was like: ‘Dad! Dad! I have two to your one!’” DeOssie said. “And he said: ‘No, son, the DeOssies have three.’ ”