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 is written from left to right. When changing direction it is not mirrored. The word that U+03A8 forms with similar adjacent characters prevents a line break inside it. The glyph can be confused with 10 other glyphs.
The Wikipedia has the following information about this codepoint:
Psi(P)SY, (P)SEE (uppercase Ψ, lowercase ψ or 𝛙; Greek: ψιpsi[ˈpsi]) is the twenty-third and penultimate letter of the Greek alphabet and is associated with a numeric value of 700. In both Classical and Modern Greek, the letter indicates the combination /ps/ (as in English word "lapse").
For Greek loanwords in Latin and modern languages with Latin alphabets, psi is usually transliterated as "ps".
The letter's origin is uncertain. It may or may not derive from the Phoenician alphabet. It appears in the 7th century BC, expressing /ps/ in the Eastern alphabets, but /kʰ/ in the Western alphabets (the sound expressed by Χ in the Eastern alphabets). In writing, the early letter appears in an angular shape ().
There were early graphical variants that omitted the stem ("chickenfoot-shaped psi" as: or ).
The Western letter (expressing /kʰ/, later /x/) was adopted into the Old Italic alphabets, and its shape is also continued into the Algiz rune of the Elder Futhark.
Psi, or its Arcadian variant or was adopted in the Latin alphabet in the form of "Antisigma" (Ↄ, ↃC, or 𐌟) during the reign of Emperor Claudius as one of the three Claudian letters. However, it was abandoned after his death.
The classical Greek letter was adopted into the early Cyrillic alphabet as "Ѱ".