have a dig at (someone or something)

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have a dig at (someone or something)

To make a mocking, sarcastic, or insulting remark, gibe, or criticism at someone's or something's expense. I'm really not trying to have a dig at you. I'm just trying to give you some constructive feedback. He's really nice to me when we hang out by ourselves, but he always starts having digs at me when we're around his other friends. I can speak the language very well, but they still can't resist having a dig at my accent.
See also: dig, have