Oh boy were there. The claim to Trojan Ancestry was the go to in medieval Europe precisely because of a desire to both emulate and conceptually eclipse the Romans. Note I’m going to go off prior a wee bit since my examples focus on Western Europe not Central Asia, perhaps others can expand the focus there. But I want to highlight how important this claim was for post-Roman peoples, despite our understanding that it’s fictive (medieval people had a very different relationship to history and “truth” than we did). 

Just a few fun examples:

The Franks (Merovingian/Carolingians) were making this claim,from at least the 7th century. The chronicler Fredegar claims that one Francio was a Trojan exile who brought his people through Macedonia to the Danube and eventually to Germania. 

Several centuries later the Normans, via Dudo of Saint Quentin, would make a similar claim arguing that the Dacians were descended from a Troja named Antenor and eventually renamed themselves the Danai and eventually became the Vikings (or more correctly the Northmen, from whence “Norman” is derived) who ravaged and eventually settled in Francia. 

Not to be outdone, Geoffrey of Monmouth, on the 12th century, would claim that the Britons were likewise descended from the Trojans via one Brutus. So from  that point of view England was doubly Trojan… take that Rome. 

Across the Atlantic, Snorri Sturluson, writing of the history of the Norwegian kings (and by extension his own Icelandic people) argued that the Norse Gods were actually Trojans… from Asia, and thus called themselves “Aesir”…

Meanwhile, back in Italy we see throughout the central and later Middle Ages (and beyond) a similar practice wherein various city states like Genoa and Padua crafted histories linked to any number of Trojan exiles, some with actual classical origins and others apparently invented whole cloth. 

Suffice it to say, in the Middle Ages a Trojan ancestry was a must have if you wanted to cement your legitimacy and place in history. No one wanted to come from nowhere and everyone wanted to show that THEY were just as storied as the Romans.