I have to display $CₓH\subscript{y}$.
Is there any chance to display a subscripted 'y' in Unicode?
\u2093 represents the subscripted 'x'
Usually you do this with formatting. Unicode's selection of superscript and subscript characters doesn't stem from the need or desire to cover whole alphabets but rather to enable specific use cases, e.g. writing IPA. Furthermore, if you're using a good OpenType font it can also support proper subscripts for arbitrary characters at the font level (where a glyph isn't simply scaled down by the layout engine, but rather a specifically-designed subscript glyph from the font is used).
In fact, since you're already using TeX or something vaguely similar to it, just let one of the many implementations render it. There are lots of things you simply cannot do in plain text without formatting, and this is one of them.
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