Could you provide some examples? I would be interested in seeing the context in which they were written
Notice in the Book of the Laws of the Countries, by Bardaisan, he distinguishes all the countries according to the laws their people follow: the laws of the Seres, the laws of the Brahmans, the laws of others in Indian, the laws of the Persions, the laws of the Bactrians, the laws of the Geli, the laws of the Racami, the laws of the Hatra, the laws of the Britons, the laws of the Parthians, and the laws of the Amazons. He then goes on to talk about the Jews and their laws. And in their case he emphasizes that they comprise a country that is not located in any one place, but that Jew, whether they be in Parthia, Arabia, or any other country, still belong to their own country according to their pursuance of the laws that make Jews Jews. And then finally, he gets to Christians and says the following (and more beyond this which I won't copy):
And what shall we say of the new race of us Christians, whom Christ at His advent planted in every country and in every region? For, lo! Wherever we are, we are all called after the one name of Christ— Christians. On one day, the first of the week, we assemble ourselves together, and on the days of the readings we abstain from taking sustenance. The brethren who are in Gaul do not take males for wives, nor those who are in Parthia two wives; nor do those who are in Judæa circumcise themselves; nor do our sisters who are among the Geli consort with strangers; nor do those brethren who are in Persia take their daughters for wives; nor do those who are in Media abandon their dead, or bury them alive, or give them as food to the dogs; nor do those who are in Edessa kill their wives or their sisters when they commit impurity, but they withdraw from them, and give them over to the judgment of God; nor do those who are in Hatra stone thieves to death; but, wherever they are, and in whatever place they are found, the laws of the several countries do not hinder them from obeying the law of their Sovereign, Christ; nor does the Fate of the celestial Governors compel them to make use of things which they regard as impure.
http://www.newadvent.org/fathers/0862.htm
Consider a similar description of Christians given in the anonymous Epistle to Diognetus. Here the author does not call Christianity a race or nation. But he compares it to races and nations and struggles to classify it. I think the closest he comes is in regarding Christians as citizens of Heaven (which goes back to the apostles):
For the Christians are distinguished from other men neither by country, nor language, nor the customs which they observe. For they neither inhabit cities of their own, nor employ a peculiar form of speech, nor lead a life which is marked out by any singularity. The course of conduct which they follow has not been devised by any speculation or deliberation of inquisitive men; nor do they, like some, proclaim themselves the advocates of any merely human doctrines. But, inhabiting Greek as well as barbarian cities, according as the lot of each of them has determined, and following the customs of the natives in respect to clothing, food, and the rest of their ordinary conduct, they display to us their wonderful and confessedly striking method of life. They dwell in their own countries, but simply as sojourners. As citizens, they share in all things with others, and yet endure all things as if foreigners. Every foreign land is to them as their native country, and every land of their birth as a land of strangers. They marry, as do all [others]; they beget children; but they do not destroy their offspring. They have a common table, but not a common bed. They are in the flesh, but they do not live after the flesh. They pass their days on earth, but they are citizens of heaven. They obey the prescribed laws, and at the same time surpass the laws by their lives. They love all men, and are persecuted by all. They are unknown and condemned; they are put to death, and restored to life. They are poor, yet make many rich; they are in lack of all things, and yet abound in all; they are dishonoured, and yet in their very dishonour are glorified. They are evil spoken of, and yet are justified; they are reviled, and bless; they are insulted, and repay the insult with honour; they do good, yet are punished as evil-doers. When punished, they rejoice as if quickened into life; they are assailed by the Jews as foreigners, and are persecuted by the Greeks; yet those who hate them are unable to assign any reason for their hatred.
http://www.newadvent.org/fathers/0101.htm
Here is the Apology of Aristides, categorizing Christians alongside Jews, Barbarians, and Greeks, again using lifestyle as the determinative factor of one's identity:
This is clear to you, O King, that there are four classes of men in this world:— Barbarians and Greeks, Jews and Christians. The Barbarians, indeed, trace the origin of their kind of religion from Kronos and from Rhea and their other gods; the Greeks, however, from Helenos, who is said to be sprung from Zeus. And by Helenos there were born Aiolos and Xuthos; and there were others descended from Inachos and Phoroneus, and lastly from the Egyptian Danaos and from Kadmos and from Dionysos.
The Jews, again, trace the origin of their race from Abraham, who begot Isaac, of whom was born Jacob. And he begot twelve sons who migrated from Syria to Egypt; and there they were called the nation of the Hebrews, by him who made their laws; and at length they were named Jews.
The Christians, then, trace the beginning of their religion from Jesus the Messiah; and he is named the Son of God Most High. And it is said that God came down from heaven, and from a Hebrew virgin assumed and clothed himself with flesh; and the Son of God lived in a daughter of man. This is taught in the gospel, as it is called, which a short time ago was preached among them; and you also if you will read therein, may perceive the power which belongs to it. This Jesus, then, was born of the race of the Hebrews; and he had twelve disciples in order that the purpose of his incarnation might in time be accomplished. But he himself was pierced by the Jews, and he died and was buried; and they say that after three days he rose and ascended to heaven. Thereupon these twelve disciples went forth throughout the known parts of the world, and kept showing his greatness with all modesty and uprightness. And hence also those of the present day who believe that preaching are called Christians, and they have become famous.
So then there are, as I said above, four classes of men:— Barbarians and Greeks, Jews and Christians.
http://www.newadvent.org/fathers/1012.htm
Now alongside these, consider the myth about the origin of the ethnicity of the Latins as told by Dionysius of Halicarnasus, a Greek who lived shortly before the time of Jesus:
60 1 After the Trojans' city was built all were extremely desirous of enjoying the mutual benefit of their new alliance. And their kings setting the example, united the excellence of the two races, the native and the foreign, by ties of marriage, Latinus giving his daughter Lavinia to Aeneas. 2 Thereupon the rest also conceived the same desire as their kings; and combining in a very brief time their customs, laws and religious ceremonies, forming ties through intermarriages and becoming mingled together in the wars they jointly waged, p201and all calling themselves by the common name of Latins, after the king of the Aborigines, they adhered so firmly to their pact that no lapse of time has yet severed them from one another.
3 The nations, therefore, which came together and shared in a common life and from which the Roman people derived their origin before the city they now inhabit was built, are these: first, the Aborigines, who drove the Sicels out of these parts and were originally Greeks from the Peloponnesus, the same who with Oenotrus removed from the country now called Arcadia, according to my opinion; then, the Pelasgians, who came from Haemonia, as it was then called, but now Thessaly; third, those who came into Italy with Evander from the city of Pallantium; after them the Epeans and Pheneats, who were part of the Peloponnesian army commanded by Hercules, with whom a Trojan element also was commingled; and, last of all, the Trojans who had escaped with Aeneas from Ilium, Dardanus and the other Trojan cities.
http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Dionysius_of_Halicarnassus/1C*.html
In the view of Dionysius, all of these people were previously from different ethnicities until they joined themselves together in this new ethnicity, named after an important founding figure. And they maintained this new identity over ensuing generations for centuries through the adoption of a set of laws and customs that would distinguish them from others.
And now, step back from those early Christians, or sideways from Dionysius, over to the apostles of Christianity's first generation, and see how they helped craft this new people group. Notice how Peter so freely uses language that formerly applied to the nation of Israel to speak of the Church, inclusive of gentiles (1 Peter 2:9):
But you are a chosen generation, a royal priesthood, a holy nation, His own special people, that you may proclaim the praises of Him who called you out of darkness into His marvelous light;
Notice the three groups into which Paul divides the world (1 Corinthians 10:32):
Give no offense, either to the Jews or to the Greeks or to the church of God,
And finally, consider Paul's two uses of the phrase "new man" (or "new humanity") in Ephesians (2:14-16 and 4:24):
14 For He Himself is our peace, who has made both one, and has broken down the middle wall of separation, 15 having abolished in His flesh the enmity, that is, the law of commandments contained in ordinances, so as to create in Himself one new man from the two, thus making peace, 16 and that He might reconcile them both to God in one body through the cross, thereby putting to death the enmity.
20 But you have not so learned Christ, 21 if indeed you have heard Him and have been taught by Him, as the truth is in Jesus: 22 that you put off, concerning your former conduct, the old man which grows corrupt according to the deceitful lusts, 23 and be renewed in the spirit of your mind, 24 and that you put on the new man which was created according to God, in true righteousness and holiness.
If I am right that Paul means the same thing by "new man" in 4:24 that he does in 2:15 (i.e. a "new human race" rather than a "new self"), then it's striking how well his conception of the Church aligns with Dionysius of Halicarnasus' conception of the formation of the Latin ethnicity.
Finally, also notice that the earliest non-Christian writer that we know of to refer to Christianity, Josephus, calls it "the tribe of the Christians" (Ant. 18.3.3). And a 4th century work claims to copy a letter written by Emperor Hadrian (so, if authentic, it reflects a view of Christians by an outsider early in the 2nd century), which says, "[Egyptians] only god is money, and this the Christians, the Jews, and, in fact, all nations adore." Notice, again, how Christians are grouped by this detractor alongside Egyptians, Jews, and all nations.
http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Historia_Augusta/Firmus_et_al*.html