Pretty sure your opening isn't over until the rooks are connected, so since castling is the usual way to accomplish that...I say the opening phase of the game unless you are deliberately delaying castling to confuse your opponent as to your intentions.
what you will prefer? Castling in start, middle or End game?
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It depends on the opening and position. In some cases castling too early can put you in trouble. The notorious panissimo pin in the Italian Game can be used to attack early castling by one side. In the other cases you want to castle early and connect your rooks.
From my opinion I will do in middle game, What about others?