Can a person on a student visa also work in a paid internship with a U.S. company in China?

I am in the process of arranging internships for students in my university's TESOL program. The students will be continuing their studies with a partner university in China while concurrently participating in an internship teaching children English. The internship is a requirement of their studies. Is it okay for the company to provide payment to the students for the hours that they work? Is the X visa the most appropriate for the students...or should we be using the F or Z? The primary reason the students will be in China is to continue their studies which will include both classes and experiential learning (i.e. internship).