The phrase "most periodically" can be replaced with a number of different synonyms depending on the context of the sentence. Some potential options include "frequently," "regularly," "repeatedly," "at regular intervals," "systematically," "habitually," and "consistently." Each of these words carries a slightly different connotation, with "frequently" suggesting a high frequency, "regularly" implying a set schedule, and "systematically" indicating a planned and organized approach. Choosing the right synonym can help to add clarity and precision to your writing, and can help readers to better understand the meaning of your sentences.