This character is a Nonspacing Mark and inherits its script property from the preceding character. It is also used in the scripts Hiragana, Katakana.
The glyph is not a composition. Its East Asian Width is wide. In bidirectional text it acts as Nonspacing Mark. When changing direction it is not mirrored. U+309A prohibits a line break before it. The glyph can be confused with one other glyph.
The Wikipedia has the following information about this codepoint:
The dakuten (Japanese: 濁点, Japanese pronunciation:[dakɯ̥teꜜɴ] or [dakɯ̥teɴ], lit. "voicing mark"), colloquially ten-ten (点々, "dots"), is a diacritic most often used in the Japanese kana syllabaries to indicate that the consonant of a mora should be pronounced voiced, for instance, on sounds that have undergone rendaku (sequential voicing).
The handakuten (半濁点, Japanese pronunciation:[handaꜜkɯ̥teɴ], lit. "half voicing mark"), colloquially maru (丸, "circle"), is a diacritic used with kana for morae pronounced with /h/ or /f/ to indicate that they should instead be pronounced with /p/.