One possible scenario in a fanfiction about Katniss' twin sister could be that she has a different set of skills. For example, while Katniss is known for her archery, the twin sister could be excellent at herbal medicine. This would add an interesting dynamic to the story as she could use her skills to help the tributes in different ways, perhaps by creating remedies for injuries or poisons. It could also change the relationship with Peeta, as the sister might have a different approach to the whole Hunger Games situation.
One unique plotline could be Prim being chosen for the Hunger Games instead of Katniss. This would completely change the dynamic as Prim is much more gentle and less trained for combat. Another could be Prim having a special connection with the Capitol's secrets, like she discovers a way to bring down their defenses through her knowledge of plants, which she uses as medicine in District 12.
She might be a mentor - like figure in the fanfiction. Since she is Katniss' twin, she has seen the brutality of the Games up close. So, she could take it upon herself to train the younger tributes from her district, teaching them not just survival skills but also the importance of unity and standing up against the Capitol. This would create a new role for her in the story and have a big impact on the future tributes from her district.
One interesting fanfiction could be where Katniss's sister, Prim, has a secret talent for combat training that she's been hiding. This could add a whole new layer to her character, as in the original she was seen as more of a healer. Another might focus on Prim's life in District 12 before Katniss volunteers for the Hunger Games, showing her daily struggles and relationships with the other villagers.
Peeta could be the one to save her. He has always cared deeply for Katniss. He might gather a group of rebels secretly and launch a rescue mission. Maybe he'll use his charm and skills to infiltrate the Capitol and find where Katniss is being held.
Gale might also attempt to rescue Katniss. He's her friend from District 12 and is quite skilled in his own right. He would be furious to hear that Cato has kidnapped Katniss and would likely gather resources and allies to try and save her.
Her character could develop a new level of determination. Before, she was fighting for her family and district. Now, with a baby on the way, she has an even greater reason to survive. She might become more calculating, using her wits to avoid dangerous situations rather than charging in head - first. She would also probably show more vulnerability, as the pregnancy adds an extra layer of stress and worry.
Katniss would likely become more protective. Her natural instinct to survive would be amplified by the need to protect her unborn child. This could make her more cautious in her actions in the arena, but also more fierce when directly threatened.
She might get angry. Katniss has a fiery side, and seeing Peeta with another girl could trigger that. She could give Peeta the cold shoulder and refuse to talk to him.
Katniss would likely be determined to get Peeta back to his normal self. So, instead of just retaliating, she would focus on finding a cure or a way to reverse the hijacking. She might isolate herself with Peeta in a safe place to try and break through to him, using her own memories and emotions to reach the real Peeta hidden inside the hijacked version.