"Z" visa for the foreigners temporarily staying in Baku

Do you have proof of residence there, such as residence permit or work permit? If not, you may ask the Chinese university to provide you an invitation letter, and apply for a China F visa. After you prove yourself competent of the job, the administration of the Chinese university may help to change your F to Z. Most Chinese universities has the capability of doing so. Of course, you have to confirm this with the university first to avoid any trouble later.