Maybe Snape's secret family consists of his mother, who is still alive but in hiding, and a younger sister he has been protecting all along. The sister could be a powerful witch in her own right, but they keep their relationship under wraps to avoid unwanted attention from the Dark forces.
His wife could be a former Hogwarts student he met during his own school days. She might be from a different house and they fell in love secretly.
His secret family could also include an elderly relative, like a grandfather. This grandfather could have passed on some important family secrets to Snape, secrets that are related to a powerful magical artifact. And the family has been guarding this artifact for generations.
Perhaps the story in the 'snape's secret family fanfiction' is centered around how Snape's secret family discovers his double life. His family might be living in a secluded place, and they start to suspect something when Snape is constantly away on 'business' for Hogwarts. They could then start to investigate and uncover the truth about his role in the fight against the Dark Lord.
It could be a long - lost son or daughter he didn't know about. Maybe a secret wife from his wilder days. There might also be a half - sibling that he never knew existed.
One possible plot twist could be that Snape's secret family has a hidden magical ability that is crucial to the wizarding world. Maybe his family has the power to reverse dark magic spells, and this is something Voldemort has been searching for all along.
If she discovers some of Snape's old potions recipes or magical knowledge, she could share it with the Hogwarts faculty and students. This would not only improve the potions classes but also make her a respected figure in the school. And her presence might also make the students re - evaluate their views on Snape, which would in turn change the overall atmosphere at Hogwarts.
It could be a random witch that Snape had a brief encounter with. Maybe she was someone he met during his time as a Death Eater or while he was spying for Dumbledore. She could have been a fellow Hogwarts student from his youth that he had a secret relationship with.
Snape's behavior could change drastically. He might become more protective of Harry if the secret was something that made Harry vulnerable. Or he could become more distant if the secret was something he disapproved of.
It could start with a lot of mistrust from Harry's family towards Snape. But as Snape shows his true intentions (if he has good ones), they might gradually warm up to him. For example, Harry's mother could see some of the good in Snape that she knew from their childhood days.
Dumbledore might come to Snape's aid. Dumbledore always had a somewhat complex relationship with Snape, and he would likely step in to prevent things from getting too out of hand. He could use his powerful magic to stop Hermione and then try to sort out the situation calmly.
In some fanfictions, Snape and Harry's secret relationship might be based on a deep, unspoken understanding. Snape, despite his outward hostility in the original story, could be portrayed as having a hidden soft spot for Harry. It might start with small acts of kindness that Harry initially misinterprets. For example, Snape might secretly protect Harry from certain threats in the wizarding world without Harry knowing. This relationship could develop over time as Harry starts to see Snape in a different light and discovers the reasons behind Snape's often - cold demeanor.