I was reading Nicolae Jorga's "History of Ottoman Empire vol. 1" and he gave an information that, Mete Khan who freed Hsiung-nu people from the rule of Yue-chi, was a servant of Chinese Emperor. But at the bottom of the page there is an editorial note saying, "During the time of Mete Khan, Huns were not serving China" The common sense about Mete Khan is, of course he wasn't serving China but from where did Jorga have the idea?
No. However, the Han Court did try to make the Hsiung'nu subservient to the Han Emperor through marriage alliances. Nicolae Iorga might have gotten the idea of Modu Chanyu (aka Mete Khan) being a Chinese servant from their wishful thinking.
In 200 B.C., Modu invaded the newly established Han China. The first Han Emperor, Liu Bang, personally led a large host north to repel the nomads. However, by feigning weakness and retreating, Modu cleverly lured the emperor into an ambush at Baideng. Liu Bang was trapped their for a week without supplies.
After this ordeal, the Emperor realised his new empire was not strong enough to confront the nomads and chose to make peace. He accepted the advice of Liu Jing, who argued that the best way to secure peace is to marry a princess to the Hsiung'nu leader. He reasoned that the Chanyu would be subservient to his father-in-law or future grandfather, the Han Emperor. The Records of the Grand Historian documented the incident as:
This is the closest that Modu Chanyu "served" the Chinese Emperor. Of course, it didn't work, especially since Liu Bang didn't want to give his daughter away.
The current Wikipedia entry for the Yue-chi depicts them as being mostly friendly trading partners with the Chinese. The (likely Turkish) Xiongnu empire built by the victorious Modu Chanyu (aka: Mete Khan, or "Brave Khan" in Turkish), was anything but.
It wouldn't be too surprising to find that histories sourced mostly from the victorious Turks are a bit dismissive of the losers. Relatively friendly trading relations would be just enough of a germ of truth to build the story around.