There are several synonyms for the phrase "poking one face in," all of which imply intruding or meddling in someone else's business. One common synonym is "butting in," which suggests an unwanted interference. Another similar phrase is "sticking one's nose in," which conveys a sense of being nosy or overly curious. "Interfering," "intruding," and "meddling" are also suitable alternatives. However, it's important to note that while these phrases carry negative connotations, there may be situations where it is appropriate to "poke one's face in" or offer assistance, advice, or support when needed.