This character is a Nonspacing Mark and inherits its script property from the preceding character. The character is also known as Greek dasia and rough breathing mark.
The glyph is not a composition. Its width in East Asian texts is determined by its context. It can be displayed wide or narrow. In bidirectional text it acts as Nonspacing Mark. When changing direction it is not mirrored. U+0314 prohibits a line break before it. The glyph can be confused with 12 other glyphs.
The Wikipedia has the following information about this codepoint:
In the polytonic orthography of Ancient Greek, the rough breathing (Ancient Greek: δασὺ πνεῦμα, romanized: dasỳ pneûma or δασεῖαdaseîa; Latin: spiritus asper) character is a diacritical mark used to indicate the presence of an /h/ sound before a vowel, diphthong, or after rho. It remained in the polytonic orthography even after the Hellenistic period, when the sound disappeared from the Greek language. In the monotonic orthography of Modern Greek phonology, in use since 1982, it is not used at all.
The absence of an /h/ sound is marked by the smooth breathing.
The character, or those with similar shape such as U+02BBʻMODIFIER LETTER TURNED COMMA, have also been used for a similar sound by Thomas Wade (and others) in the Wade–Giles system of romanization for Mandarin Chinese. Herbert Giles and others have used a left (opening) curved single quotation mark for the same purpose; the apostrophe, backtick, and visually similar characters are often seen as well.