The correct preposition here is "on," because when describing the position of a door relative to a person, it is most natural to say "the door closed on him."
Step 2: Evaluating the Other Options
"Beneath" (Option A) would imply something below him, but the context suggests the door is closing in relation to his position.
"Between" (Option B) would only apply if the door were closing between two entities, which is not the case here.
"Amidst" (Option C) typically refers to something being surrounded by other things, which doesn’t fit in this context.
Step 3: Conclusion
Thus, the correct preposition is "on," making the sentence: "The door closed on him."