Medieval China? So are we talking more Ming, Yuan, Tang, or Song dynasties? I've only put out those dynasties as they're the major imperial dynasties that ruled over the bulk of medieval China-proper instead of one of the many times China broke. I'm guessing more Yuan since the Mongols were the ones that actually ruled over Tibet under what was essentially a major successor of imperial China and the Mongol Empire. Unless you go into the early modern era in which the Qing would be a good candidate. In fact, considering A'therys has a range of influences that go up to the early 20th century (thank you Alor radio for the benchmark), the Qing might be appropriate.
Also, now that I know Daidama is more of a China-based nation I can potentially justify an Alor trade/treaty port there! <3 <3 <3