It seems you are looking for a story inspired by of the English dub of Shinobi no Ittoki . In this episode, titled "Cycle of Fate," the tension between the Iga and Koga clans reaches a boiling point during the Ninja Academy exams.
"The Iga heir," Haruka sneered, spinning a kunai between his fingers. "A boy playing dress-up. Do you think that suit makes you a ninja? You’re just a relic of a dying clan." Shinobi no Ittoki (Dub) Episode 5
Here is a story expanding on the themes of that episode, focusing on the weight of heritage and the "cycle" that traps these young ninjas. The Weight of the Blade It seems you are looking for a story
The battle that followed was a blur of high-tech gadgetry and ancient martial arts. Haruka was faster, his movements honed by years of brutal Koga conditioning. But Ittoki had something the Koga lacked: a reason to live beyond the kill. He didn't want to conquer; he wanted to protect the small, quiet life he had left behind. "A boy playing dress-up
Haruka hit the ground, gasping for air. Ittoki stood over him, his breathing ragged. He had the opening. He could have ended the cycle right there.