Perhaps in the fanfiction, there's a misunderstanding. Sakura believes Ino has done something wrong, but she's actually wrong herself. She goes after Ino with the intention of teaching her a 'lesson'. Naruto, who has a good heart and is friends with both of them, realizes Sakura's mistake. He uses his speed and strength to get between them and saves Ino. Naruto's sense of justice and friendship drives him to protect Ino from Sakura's unjust actions.
In some fanfictions, Naruto might save Ino from Sakura if there's a situation where Sakura is, say, being overly aggressive or misdirected in her actions. For example, if Sakura accidentally uses a jutsu that endangers Ino during a training session, Naruto could use his quick reflexes and his own jutsu to block the attack and save Ino. Another possibility could be in a more complex plot where Sakura is under some sort of mind - control and Naruto has to step in to protect Ino from her.
Well, it could be that Sakura is jealous of Ino for some reason in the fanfiction. Maybe she thinks Ino is getting too close to Sasuke or Naruto. So, she tries to harm Ino in a fit of rage. Naruto, being the hero he is, senses the danger and jumps in to save Ino. He might use his Rasengan or some other powerful technique to stop Sakura's attack. It all depends on how the author of the fanfiction has set up the characters' relationships and the overall plot.