One common type is friendship conflict. For example, two friends might have a falling out because of jealousy over a new friend or a difference in interests. Another type is academic competition conflict. In some novels, students compete for the top grades or a scholarship, which can lead to rivalry and conflict.
There's also the conflict between students and teachers. In novels, it could be about strict rules or unfair grading. A student might feel that a teacher is being too harsh, which causes tension. Also, social status conflict is quite common. Middle school is a time when social hierarchies start to form. So, in novels, there can be conflict between the popular kids and the outcasts, or between different cliques.