It could be that they were tricked into thinking they were helping someone. A villain might have convinced them that the 'kidnapped' person was a bad guy who needed to be taken away for interrogation. But as the story unfolds, they realize they've been used and have to find a way to make things right.
It could be April. Since she's a human and often involved with the Turtles' adventures, she might be an easy target. Maybe the bad guys convinced Mikey and Donnie that April was in some way endangering them.
While Mikey and Donnie are the main focus, sometimes their older brothers Leo and Raph can also play important roles in the fanfiction. For example, they might be searching for the missing baby turtles, or they could be the ones who teach Mikey and Donnie important lessons when they finally reunite.
One interesting plot could be baby Mikey and Donnie getting lost in the sewers while exploring on their own. They have to use their wits and the little skills they've learned to find their way back to their brothers.
One possible plot twist could be that Mikey was kidnapped by an unexpected enemy, like a former ally who turned bad. Maybe it was someone he trusted, and this betrayal adds a layer of drama.
In this fanfiction, the plot might revolve around the mystery of how April got pregnant in the first place. Since they are from different species, it could be some sort of magical or scientific anomaly. Donnie would be on a quest to understand it while also taking care of April. They could also have to deal with the reactions of the human world if the pregnancy becomes known. There could be a sub - plot where they search for a safe place to raise the baby, away from both human and mutant threats.
In a fanfiction, Mikey might get hurt during a mission to infiltrate a Kraang base. He could be detected by security systems and get zapped by some sort of electric defense mechanism. This would leave him weak and in pain. His brothers would need to carry him out of there and find a way to reverse the effects of the zap. They'd be desperate to get Mikey back to his normal, energetic self.
I'm not sure specifically as I haven't read this particular fanfiction. But it might be about Mikey from the Teenage Mutant Ninja Turtles getting some sort of skin condition like shellacne. It could involve his friends helping him deal with it, or his own journey in handling this new and unexpected situation.
In many 'TMNT Mikey hurt' fanfictions, a common plot element is Mikey's own attitude towards his injury. Sometimes he tries to be brave and not show how much pain he's in to not worry his brothers. Another element is the search for a cure or solution. If he's poisoned, they'll look for an antidote. If it's a physical wound, they'll try to find medical supplies or a way to heal it. And there's usually a lot of brotherly bonding as they take care of Mikey.
One possible scenario could be that Mikey gets hurt during a fight with the Foot Clan. Maybe he underestimated an opponent and got a nasty cut on his arm. His brothers would then rush to his side, with Donnie trying to patch him up as quickly as possible while Leo and Raph stand guard, ready to fend off any further attacks.
Well, his brothers would probably go on a wild rescue mission. They'd search every nook and cranny of the city. Maybe they'd get some help from April and Casey too.