3 : a going back in time or upward in order of genealogical succession
1 : a : derivation from an ancestor
Which should I use to refer to someone who has a, let's say Chinese, origin:
a person of Chinese descent, or
a person of Chinese ascent ?
You should use descent for this. We say that a person descends from their ancestors, or that a person is descended from their ancestors. A person's descent refers to their ancestral line as a whole.
I am a person of Chinese descent.
You could also use "ancestry" or "heritage" as close synonyms. The latter emphasizes the cultural influence over the genealogical influence.
The only place I've heard ascent used in any genealogical sense is to refer to the evolutionary or sociological progress of a species or civilization, as in "the ascent of Man." This is just a fancier way of saying "the rise of Man."