and again a little later in Book 3:After the martyrdom of James and the conquest of Jerusalem which immediately followed, it is said that those of the apostles and disciples of the Lord that were still living came together from all directions with those that were related to the Lord according to the flesh (for the majority of them also were still alive) to take counsel as to who was worthy to succeed James. They all with one consent pronounced Symeon, the son of Clopas, of whom the Gospel also makes mention; to be worthy of the episcopal throne of that parish. He was a cousin, as they say, of the Saviour. For Hegesippus records that Clopas was a brother of Joseph. He also relates that Vespasian after the conquest of Jerusalem gave orders that all that belonged to the lineage of David should be sought out, in order that none of the royal race might be left among the Jews; and in consequence of this a most terrible persecution again hung over the Jews.
and again:But when this same Domitian had commanded that the descendants of David should be slain, an ancient tradition says that some of the heretics brought accusation against the descendants of Jude (said to have been a brother of the Saviour according to the flesh), on the ground that they were of the lineage of David and were related to Christ himself. Hegesippus relates these facts in the following words. Of the family of the Lord there were still living the grandchildren of Jude, who is said to have been the Lord's brother according to the flesh. Information was given that they belonged to the family of David, and they were brought to the Emperor Domitian by the Evocatus. For Domitian feared the coming of Christ as Herod also had feared it. And he asked them if they were descendants of David, and they confessed that they were. Then he asked them how much property they had, or how much money they owned. And both of them answered that they had only nine thousand denarii, half of which belonged to each of them. And this property did not consist of silver, but of a piece of land which contained only thirty-nine acres, and from which they raised their taxes and supported themselves by their own labor. Then they showed their hands, exhibiting the hardness of their bodies and the callousness produced upon their hands by continuous toil as evidence of their own labor. And when they were asked concerning Christ and his kingdom, of what sort it was and where and when it was to appear, they answered that it was not a temporal nor an earthly kingdom, but a heavenly and angelic one, which would appear at the end of the world, when he should come in glory to judge the quick and the dead, and to give unto every one according to his works. Upon hearing this, Domitian did not pass judgment against them, but, despising them as of no account, he let them go, and by a decree put a stop to the persecution of the Church. But when they were released they ruled the churches because they were witnesses and were also relatives of the Lord. And peace being established, they lived until the time of Trajan. These things are related by Hegesippus.
In other words, Hegesippus seems to have a discernible structure. The descendants of Jesus all lived until the age of Trajan. In this reference it is implied that even though both Vespasian and Domitian had "sought out" the line of David intending to kill them, and members of the lineage 'bore testimony before them' - it was only in the age of Trajan that the line was wiped out.It is reported that after the age of Nero and Domitian, under the emperor whose times we are now recording, a persecution was stirred up against us in certain cities in consequence of a popular uprising. In this persecution we have understood that Symeon, the son of Clopas, who, as we have shown, was the second bishop of the church of Jerusalem, suffered martyrdom. Hegesippus, whose words we have already quoted in various places, is a witness to this fact also. Speaking of certain heretics he adds that Symeon was accused by them at this time; and since it was clear that he was a Christian, he was tortured in various ways for many days, and astonished even the judge himself and his attendants in the highest degree, and finally he suffered a death similar to that of our Lord. But there is nothing like hearing the historian himself, who writes as follows: Certain of these heretics brought accusation against Symeon, the son of Clopas, on the ground that he was a descendant of David and a Christian; and thus he suffered martyrdom, at the age of one hundred and twenty years, while Trajan was emperor and Atticus governor. And the same writer says that his accusers also, when search was made for the descendants of David, were arrested as belonging to that family. And it might be reasonably assumed that Symeon was one of those that saw and heard the Lord, judging from the length of his life, and from the fact that the Gospel makes mention of Mary, the wife of Clopas, who was the father of Symeon, as has been already shown. The same historian says that there were also others, descended from one of the so-called brothers of the Saviour, whose name was Judas, who, after they had borne testimony before Domitian, as has been already recorded, in behalf of faith in Christ, lived until the same reign. He writes as follows: They came, therefore, and took the lead of every church as witnesses and as relatives of the Lord. And profound peace being established in every church, they remained until the reign of the Emperor Trajan, and until the above-mentioned Symeon, son of Clopas, an uncle of the Lord, was informed against by the heretics, and was himself in like manner accused for the same cause before the governor Atticus. And after being tortured for many days he suffered martyrdom, and all, including even the proconsul, marveled that, at the age of one hundred and twenty years, he could endure so much. And orders were given that he should be crucified. In addition to these things the same man, while recounting the events of that period, records that the Church up to that time had remained a pure and uncorrupted virgin, since, if there were any that attempted to corrupt the sound norm of the preaching of salvation, they lay until then concealed in obscure darkness. But when the sacred college of apostles had suffered death in various forms, and the generation of those that had been deemed worthy to hear the inspired wisdom with their own ears had passed away, then the league of godless error took its rise as a result of the folly of heretical teachers, who, because none of the apostles was still living, attempted henceforth, with a bold face, to proclaim, in opposition to the preaching of the truth, the 'knowledge which is falsely so-called.'
Here is one difficulty with that. It would appear that Julius Africanus makes mention of meeting members of the lineage of Jesus. Africanus also used Hegesippus. Surely he would have had to provide an explanation for his statement if Hegesippus was taken to mean - 'all the descendants of Jesus were killed by Trajan.' Also when I look at Eusebius's citations above there can't have been much more written about the line of David. It wasn't like pages and pages were written about what happened to the Church of Jerusalem and Eusebius cites only a fraction of what was written. This was pretty much it.
So basically this is what Hegesippus said about the Jerusalem Church:
1. the descendants of Jesus came together after the death of James and unanimously elected Symeon the son of Clopas bishop, Clopas being the brother of Jesus's father Joseph
2. Vespasian launched an effort to wipe out the family of David after 70 CE and this persecution was imagined to affect 'the Jews' as such - "a most terrible persecution again hung over the Jews."
3. Domitian launched a fresh effort to wipe out the lineage after heretics (perhaps specifically Jewish individuals). The effort was directed against descendants of Jesus's brother Jud(as). Hegesippus saw this as an extension of Herod's fear about the coming of Christ. In the end Domitian changed his mind and let them go. The ultimate persecution was said to have taken place under Trajan.
4. Trajan crucified Symeon under Atticus c. 99–102 CE. The persecution under Trajan was prompted by 'heretics' owing to their status as descendants of David and the fact they were Christians. I strongly suspect that these 'heretics' were Jews and the text was written from the perspective that the descendants of David were rightly the rulers of the Jewish people. Hegesippus distinguishes between two classes of heresies - (a) 'ancient' heresies that led to the familiar division of Pharisees, Sadducees etc. and (b) the heresies which occurred after the events of the gospel - viz. "Thebuthis, because he was not made bishop, began to corrupt it. He also was sprung from the seven sects among the people, like Simon, from whom came the Simonians, and Cleobius, from whom came the Cleobians, and Dositheus, from whom came the Dositheans, and Gorthæus, from whom came the Goratheni, and Masbotheus, from whom came the Masbothæans."
I don't see any evidence that Hegesippus there were no more descendants of Jesus after Trajan. Just that there was a persecution which led to the crucifixion of Symeon and death to the descendants of Jude (both of which seem to have been introduced earlier in the narrative).