A friend of mine recently told me that once, he checkmated his opponent and then immediately resigned, because he thought his win unfair. This happened in a FIDE-rated tournament.
Searching the FIDE Laws of Chess, I found (emphasis mine):
1.2 The objective of each player is to place the opponent's king 'under attack' in such a way that the opponent has no legal move. The player who achieves this goal is said to have 'checkmated' the opponent's king and to have won the game. [...] The opponent whose king has been checkmated has lost the game.
5.1 The game is won by the player who has checkmated his opponent's king. This immediately ends the game, provided that the move producing the checkmate position was a legal move.
Is this possible in any way, for example move the piece, don't press the clock and then resign?