What is the adverb for school?

There isn't a single perfect adverb directly derived from "school." The best adverbial phrase depends on the context. You might use phrases like:

* In school: (e.g., "He learned that in school.")

* At school: (e.g., "She's at school right now.")

* Scholastically: (This refers to academics and schoolwork)

There's no single word adverb equivalent to "school-ly" or similar.