The phrase "have digs at" is commonly used to describe someone making critical or negative comments towards someone else. However, there are several synonyms that can be used instead of this phrase. One can "mock" or "taunt" someone instead of having digs at them. Additionally, one can "ridicule" or "berate" someone, which are stronger options to convey criticism. One can also "denigrate" or "disparage" someone in a more formal setting, or "chide" or "rebuke" them in a more authoritative role. Using these synonyms can add a unique touch to one's language and make it more expressive.