Can Chinese born baby with Singapore passport apply long stay visa to stay with the Chinese mother?

My Chinese wife born our baby in Zhengzhou, Henan province in China. When she wants to bring the baby back to PRC, we know the baby needs to apply one for staying not more than 30 days.

What if she wants the baby to stay a few months to a year with her in PRC? Can the baby extend itaccordingly? And if my China wife household account is in Dengzhou, can she apply the extension in Zhengzhou?

Thanks