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This chapter can be found on AO3 Here
Summary:
Izuku is a Legacy Student at UA. He just doesn't know it.
Or the one where Aizawa has a son and doesn't know it. Until he does.
Inko remembers being young and foolish, and finding a hero in her apartment dumpster. She remembers a young man with dark hair and dark eyes and gentle, but calloused hands. She remembers seven nights of worry as she nursed him back to health and two nights of bliss before he left. She remembers promises whispered in the dark, and the heat of devotion as it pierced her to her very core. She remembers the day he walked out her door, leaving no way to reach him, and the call from her grandfather's lawyers. She sells the house her grandfather left her, and as her belly begins to swell, she married the man who had chased her, and thanked every kami she can think of that her baby looks like her. She sheds no tears when after two years overseas, when her baby is four, Midoriya Hiashi sends her the divorce papers. Inko raises her boy as best she can, teaches him as best as she can, and cries whenever Izuku nullifies her Quirk in a burst of emotion, because even if he had returned, he would find an empty apartment. If he looked in on her, he would find a married woman with a child and an estranged husband overseas, divorce still pending. She is raising her baby and living off her dwindling inheritance, and she is alone.
She deliberately takes Izuku to a doctor with a reputation for using the toe joint as gospel for identifying quirks. She cries and apologizes over and over to Izuku, because she knows the doctor has misdiagnosed her baby, because Izuku has been nullifying quirks when emotional for years. She hopes that with label quirkless, he'll never be a hero. He won't ever cross paths with that person. Inko is selfish, and she knows it.
Years later, when Izuku suddenly develops a strength augmentation quirk, Inko is suspicious. But her baby boy is so happy after years of believing himself quirkless, she can't bring herself to stamp out his happiness. She lets him go to UA and dreads the day that man comes storming in, demanding to know why she kept his son from him.
When he does come, he does not give any sign of knowing her. He is blank faced even as he tells her what she already knows, that Izuku has a quirk under the strength augmentation, that he can nullify quirks.
Her boy grows into a fine young man under the tutelage of his father and All Might.
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Shouta remembers being less than observant of his surroundings and blacking out after being thrown off a roof into a thankfully half filled dumpster. He remembers waking in a warm bed, his injuries tended to, and a young woman with the face of an angel. He remembers seven nights of healing, of falling in love, two nights of bliss, of promises whispered into the dark and the searing heat of devotion that stole the breath from his lungs. He walks out her door, leaving her no way to reach him, and his promise to return. And return he does after eight months of tracking and shutting down cartels spreading around illegal quirk enhancing drugs, to an apartment inhabited by a new person, the work of four months tracking her footsteps, and finding a woman married with a baby at the breast. He turns his back, brokenhearted.
Fourteen years later, Shouta sees him. The boy looks so much like her that it breaks his heart, and his smile is so sweet, it takes his breath away. This is her boy, the boy that could have been his.
Terror grips his heart as the villain with the disintegration quirk reaches for the boy. His last sight as his face caves in under the monster's blow is of five fingers touching the boy's face, the face that looks so much like hers.
The boy has a quirk under One for All. He can nullify quirks. It is on a whim that he asks Recovery Girl to run the tests. He doesn't expect them to come back positive. Except they do.
The Problem Child is Shouta's son.
He keeps it secret. All Might finds out by accident.
Shouta doesn't approach the Midoriya apartment if he can help it.
Shouta nearly has a heart attack the first time the Problem Child calls him "Dad." Afterwards, it's all he can do to keep a straight face, because his son is calling him "dad!" He doesn't know Shouta is his father, but still!
Izuku grows into an excellent hero. One worthy of succeeding All Might.
Shouta has never been prouder.