There are four kinds en passant checkmates-
- The pawn moves, checking the king itself.
- The pawn moves, checking the king, while also allowing another piece to check as well, aka a double check.
- The pawn moves, not checking the king, as to allow another piece to check the king, aka a discovered check.
- The pawn moves, not checking the king itself, as to allow two other pieces to check the king, aka a double discovered check.
Here are the fastest possible games for all four categories, in order. Variations exist of course. To get the fasest checkmates for black, simply reverse each game, always adding on a half a move.
Sources: The Lichess Forums & The Chess Problem Database
1. e4 f5 2. exf5 Kf7 3. Qg4 h6 4. b3 Qe8 5. Bb2 g5 6. fxg6#
1. e4 d5 2. d4 dxe4 3. d5 Kd7 4. Bc4 Nc6 5. Bg5 Qe8 6. h3 e5 7. dxe6#
1. e4 e5 2. g4 Nc6 3. g5 d6 4. Qh5 Kd7 5. Bh3+ f5 6. gxf6#
1. c3 f5 2. h4 Kf7 3. Qb3+ Kg6 4. Qf7+ Kh6 5. h5 a6 6. d4+ g5 7. hxg6#