On Amethyst, selecting the 'boost' icon gives two options; boost or quote.

However, you can also do it 'old school' (i.e. manually) by getting the note ID of the note you want to quote and simply embed that ID text in your new note.

What client are you using?

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Damus on iOS and Iris on Windows, and I've tried rhe intuitive old school method you mention, to no avail.

Yeah, every client handles it differently. Nostrgram, for example, has a "quote" button you can click. If you write something, it's a quote tweet. If you send it without writing anything, it's a boost.