can my wife apply for S1 visa as my son is studying in China and will it be multiple?

Gripson, your wife can apply for the S1. It is actually a single entry one with the duration of stay of 30 days. She just needs to change it into a long-term resident permit within 30 days after she arrives.

In order to apply for the S1, the invitation letter from her son and copies of his passport and valid resident permit are required. Meanwhile, she has to prepare the kinship certificate (her son's birth certificate). As for the permission, I think you should ask your son to consult with his university.

At last, she should have the birth certificate notarized and authenticated by your Minsitry of Foreign Affairs and then get it authenticated by Chinese embassy. The authenticated version is required when she changes S1 into a resident permit.