So it's actually quite difficult to identify what we call Han or ethnic "Chinese" in the Roman empire and Medieval Europe. The primary way is through DNA, but that technique is actually rather rarely used, to most people's surprise. Mostly two techniques are used: Skull Morphology, which is used to identify specific features in human skulls in order to determine if they're of European, Asiatic, or African ancestry. The other is Osteography, which uses isotopic analysis to determine where someone grew up based on comparing isotopes in their teeth to geological samples.

DNA can tell you straight up whether someone is Chinese, Mongol, etc. etc. Skull Morphology and Osteography can tell you that information to a certain degree, you can compare it to average population samples. But it can't tell you that definitively like DNA can, and even DNA technically can't tell you that definitively. A Chinese man living with the Huns may identify as a Hun, even though he's genetically from the Yellow River area.

Now, that being said, we have identified skulls of Asiatic ancestry in Western Europe. Determining whether or not they are ethnically Chinese is a different matter. Redfern et. al. (https://www.sciencedirect.com/science/article/pii/S0305440315003167) found evidence of two 3rd century persons using Osteographic analysis that they had likely East Asian ancestry. However, follow-up research has found that they actually originated from the Hexi Gansu region (the corridor between China Proper and Chinese Turkestan aka Xinjiang).

Just because someone is found to be east Asian doesn't mean they actually grew up there either. Their parents very well could have immigrated, and then they could have grown up in Sogdia, or the Pontic steppes, or Syria. So determining and individual's origin and the degree of mobility of individuals in the empire and medieval Europe isn't easy.

However, this is a later Roman example, and maybe someone can provide examples from "medieval Europe" proper (i.e. the 8th-15th centuries).