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The short answer is "None". There's no official record exist in history texts during and after Yuan dynasty about a foreigner lives in the court of Kublai Khan, who was favored by the Khan, who was made a government official in Yang Zhou city, and then accompanied a princess on her wedding trip.

The thing is, we Chinese LOVE our history. It's not just the ruling class, it's a culture, a beloved tradition. China has always placed history record on an very important place. We believe by learning from history we can make a better tomorrow. China is the first civilization that set up a government position for court historians. Even during foreign invasion when imperial records might be lacking or missing, local governments would maintain chronicles for the city or province.

So, if a foreigner who had been living in Kublai Khan's palace, who had been appointed as local officials, who had been send on important diplomatic missions accompany members of royal family, we will have some kind of record of him exist somewhere.

But no... sadly, we don't.

As a result, there has always been controversy surrounding whether Marco Polo had actually made it to China, and even if he did, he might not be nearly as important as he proclaimed to be. Almost all modern Chinese historians believe Marco Polo never reached China, not only because the lack of Chinese historical records on his existence, but also because his book had a lot of holes that make it more like a hearsay than actual witness testimony. For example, many had pointed out Marco Polo had not mentioned tea, chopsticks, the great wall, etc.

However, it also worth mention that he didn't write the Travels of Marco Polo himself. It's never intended to be a truthful memoir of his journeys. He told his story to Rustichello da Pisa while both of them were in jail, most likely to pass time. It could be that in favor of telling interesting stories, he mixed what he had heard and what he had experiences together plus a bit imagination (princess? really?). It could be that he never actually reached China, but he did traveled a lot, met a lot of interesting people, and he stitched stories together and put all of them on himself.

So here's my theory:

Marco Polo had indeed reached 元大都 (current Beijing) China. He probably traveled a bit in the surrounding areas. But he never entered the court of Kublai Khan. He had never received any official appointment, he never went to Yang Zhou (which was in southern China), and he had never met the princess. But he was in north China for awhile, he saw a lot of interesting stuff. He heard even more stories. His book is comprehensive and consistent enough that it's very unlikely he heard all of it from stories of other people. But his Travel had indeed exaggerated greatly of his own importance and the places he had visited in China. And when in jail and had nothing to do, he started telling insane stories.

And... we're left with the Travels of Marco Polo, and all Chinese believe pizza pie is Marco Polo's failed attempt to make a Chinese 馅饼. Only he forget how to keep the stuffing inside, so poor Italians end up with the stuffing on top of the dough.

Pizza pie made right!