which visa should i apply? study (X) or travel or employment?

You need to apply for a Business Visa (F visa) to do your fellowship for a duration of 3 weeks.

F Visa: Issued to an applicant who is invited to China for visit, research, lecture, business, scientific-technological and culture exchanges or short-term advanced studies or intern practice for a period of no more than six months.

if i want to go china for 6months what is want please give me all information what is need and how much money i pay

You also need to apply for business visa (F visa) if you go to China for 6 months, you first need to get an invitation letter from China side, your question is not clear, can you clarify it and tell me more information of the purpose of coming to China?