take a dig at
take 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 take 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 taking digs at me when we're around his other friends. I can speak the language very well, but they still can't resist taking a dig at my accent.
take a dig at someoneand take a jab at someone; take digs at someone
Fig. to insult or pester someone. Why did you take a jab at Sam? You're always taking digs at people who think they're your friends. Jane is always taking digs at Bob, but she never really means any harm.