The string appears to be a cryptic clue in the style of a cryptic crossword.
But without more context, the cleanest match to a 3-letter "piece" is (as in a piece of something) — but the wordplay "twbydy" doesn't yield that. twbydy-am-by-3
But: if this is a from a larger set, and the answer length is given as 3 letters, then "by 3" means the word is 3 letters long, and the preceding text gives the wordplay. The string appears to be a cryptic clue
Given the cryptic style, I suspect ; "am" = morning = "AM"; "by" = next to; "3" = three letters; total maybe "FOUR AM" → anagram? "am" = morning = "AM"