The opposite of "most regularly" is irregularly, meaning not occurring at regular intervals or in a consistent pattern. Some synonyms for irregularly include sporadically, infrequently, or haphazardly. Another antonym could be unpredictably, indicating that the frequency or timing of events is not easily anticipated or planned. "Occasionally" could also be used as an antonym, suggesting that an event or action happens only once in a while, without any particular schedule or pattern. Overall, the antonyms for "most regularly" describe events or behaviors that are inconsistent or unpredictable, rather than characterized by a steady, consistent routine.