The boy asked his teacher, “_____ come in?”

The correct answer is: May I

The boy asked the teacher whether to come in or not. He asked by asking May I. It denotes that the teacher may allow him inside the class or he may not allow him. It depends on the way of asking by the boy. The boy is polite in his manner. The allowance of the boy inside the class depends on the situation of the class and the teacher. So, by asking politely, the teacher may allow him.