Choose the correct modal to fill in the blank: He ______ not enter my house…

The correct modal to fill in the blank is shall. The full sentence is: "He shall not enter my house again."

Grammatical Explanation: Modals for Command
While "shall" is often associated with simple future tense for the first person ("I," "we"), it takes on a different role in formal grammar when used with the second and third persons ("you," "he," "she," "it," "they").

Expressing Command: When used with the second or third person, "shall" is the standard modal to express an authoritative command, threat, promise, or a sense of strong determination.

Why it fits here: The context clue in the bracket is (Command). By using "shall," the speaker is asserting firm authority, making the statement a direct prohibition rather than a simple future prediction.