Before you can answer that question, you have to begin with, "Who are the Trojans?". And this question is not so easy as you might initially think.
Anthropologists today pretty much define ethnicity exclusively in terms of ascription-- Does a person self-ascribe as a certain ethnicity, and do outsiders ascribe that same ethnicity to that person? If this is the case, they can be said to belong to that ethnicity.
Of course, when someone self-identifies as an ethnic group, there is the tendency to act in ways that delineate boundaries between the in-group and the outside. Dressing a certain way, eating a certain way, or talking a certain way are all examples of acts designed to create and enforce boundaries. This is especially prevalent in border areas, where different ethnic groups come in frequent contact.
SO, for a long time archaeologists have thought that if you can identify materials that are strongly associated with a supposed ethnic group, then you can reasonably say that you are probably digging where that ethnic group once lived. For example, if you're digging a settlement with Greek writing, greek style architecture, and pottery sourced to clay deposits in Greece, then you're probably dealing with Greek ethnicity.
In general, this is a good start for studying ancient ethnicity.
But there are three problems with this-- one, these "ethnic groups" like the Thracians or the Scythians or the Trojans may only have ever existed from the point of view of the people writing about them. While the Greeks might have considered the Trojans to be the people across the Aegean in the city of Troy, in reality, it could be that there were multiple groups of people in the city who self-identified as various things.
two, acts (and therefore material culture) that stress a certain ethnicity are almost never exclusive, and it's impossible to know if they were meaningful in the past in daily life. Sure, some Thracians may have used scythe-like sica style swords. But many other groups probably did too. It could be that the style of sword, which modern classicists use to guess about a cultural identity, was actually not what was most important for the Thracians for defining their own ethnic boundaries. They might not have given a second thought to their type of sword, in fact, it could have been more about language and burial customs. Who knows.
three, even with living societies, an ethnic group is still extremely difficult for anthropologists to define. Ethnic groups are porous, with people moving in and out of them depending on the social situation, politics of the day, geographic location, or time of year (you may be one ethnicity when you're driving your sheep in the spring, but another when you're settled in at the farm in the fall). Ethnicity is also relative, and dependent on perspective. To immigrant American Kurds, all Kurdish speakers in Kurdistan are Kurds. But in Kurdistan itself, there are other divisions, based on who farms, who herds, who lives in tents, who lives in cities.
So if it's hard to establish ethnicity even in the present day, when you can just go up and ask people, "How do you identify?", consider how hard it is to actually get at ancient ethnicity, where the whole population is long gone.
In conclusion, the Trojans really only exist to us as characters in a history book. Finding their descendents relies on finding the Trojans themselves, which is not something I think we can do archaeologically.
We know basically nothing about the ethnicity of the people who lived in Troy I through to Troy VII, as they left no written records; our only clues are that they tended to use Anatolian styles of pottery, and in ca. 1400-1170 BCE they were an adjunct to the Hittite Empire, first as a buffer state, later as a vassal/member state. After that the city dwindled away until it was abandoned ca. 950 BCE, but we know even less [edit] at that period.
Greek colonisation of the Troad began in the 8th century BCE. We don't actually know which Greeks settled the Troad; probably Aeolians, but we can't be sure because the ethnic picture of the area was messy at the time. The Troad was never considered to be part of "Aiolis", the area of Asia Minor dominated by Aeolian Greeks, which included Smyrna not far south of Troy. Based on this it's likely that the Greeks never dominated the Troad in the same way that they did at Smyrna: it had a more mixed ethnicity. This mix may have included
The reason why I suggest a mix of three ethnicities is this business of the Aeolians not dominating the Troad in the way they did the area just to the south. A cluster of at least three ethnic groups would seem to explain this better than a Greek overlay on a single native population. In addition, the Trojan catalogue in the Iliad attests to what 7th-century Greeks thought about the ethnic make-up of the area, and that firmly indicates an informal anti-Greek alliance of Mysians, Lelegians, and other peoples from further afield. Other possibilities for inclusion in this ethnic cluster that I'm suggesting would be Thracians (from across the Hellespont) and Phrygians (from central western Anatolia).
There's no hard evidence for this cluster of ethnicities, but hard evidence just isn't available. No specific, distinctive ethnic identity was associated with the Troad in the historical period. One possible exception is that some folks have argued that there was a dynasty of so-called Aeneadae in the area; no one's suggesting that we take seriously the idea of descent from a historical Aineias, but it's possible that a dynasty existed that made that claim. Unfortunately even the evidence for the Aeneadae is doubtful.
Whatever the reality, the basic upshot is that, whatever ethnic identity Troy/Wilusa had in the late Bronze Age, it was diluted by the time of Greek colonisation, whether just mildly diluted, or diluted to the point of non-existence. The city itself was abandoned ca. 950, remember. When Greeks came along and colonised the area -- not fully successfully, it seems -- that only accelerated the process of dilution.
(There's no reason to take seriously any of the legends about Trojan migration after a supposed Trojan War. They're not compatible with the fact that the city was still inhabited into the 10th century, anyway.)
The British have a literary tradition of tying themselves to Trojans, starting in the 9th century with the Historia Brittonum, but it is more well established with the 1136 Historia Regum Britannia by Geoffrey of Monmouth.
It's only an interesting literary tradition; the historical value of the Brut legend is pretty much nil.
Purely from a literary/mythological standpoint, Virgil's Aeneid has the surviving Trojans sail to Italy. Aeneas - one of the heroes of the Trojan army, relative to King Priam, Hector, and Paris, and son of Venus - led them there and married the Latin princess Lavinia.
They founded the city of Lavinium and their descendents eventually led to Romulus and Remus the founders of Rome. Eventually the family line connects with Julius and Augustus.
I'm going to reiterate though, this is all through literature and mythology.