There is no exact equivalent of the schwa sound [ə] in Mandarin Chinese. Mandarin Chinese has a relatively small set of vowels, and the mid central vowel [ə] is not among them.
The closest Mandarin Chinese vowel to schwa would be [ɤ], which is a mid back unrounded vowel. It is written as 'e' in the Pinyin romanization system. This vowel [ɤ] can appear in unstressed syllables in Mandarin, similar to the role of schwa in English.
However, there are some key differences:
[ɤ] can still carry one of the four Mandarin tones, whereas schwa is typically toneless.
[ɤ] does not reduce or centralize other vowels in Mandarin the way schwa does in English. The Mandarin vowel system remains largely intact in unstressed syllables.
[ɤ] does not have the same degree of variability and contextual dependence as schwa. It has a more consistent quality across contexts.
So in summary, while [ɤ] shares some of the phonetic and phonological behavior of schwa, there are also some significant differences. Mandarin lacks a true equivalent of the schwa found in English and some other languages.