In these fanfictions, a prevalent trope is the 'mystery of the past'. Writers often explore how Hermione's true parentage was hidden and what led to it. There's also the 'protective Snape' trope. Despite his cold exterior, he becomes fiercely protective of Hermione once he knows she's his daughter. The 'identity crisis' trope is also quite common. Hermione struggles with her Gryffindor values while also having Snape as her father, who was a Slytherin. This creates a lot of internal conflict for her and is often explored in great detail in these fanfictions.
Typical tropes include the 'revelation shock'. When Hermione first discovers she's Snape's daughter, there's usually a big moment of shock and disbelief. Also, the 'finding common ground' trope is often used. As they get to know each other as father - daughter, they find similarities in their personalities or magical abilities. And don't forget the 'changing relationships' trope, especially with her friends who now have to adjust to this new Hermione.