Were any of the Apostolic Fathers Jews? A simple question; I am reading the Apostolic Fathers and have noticed how they frequently refer to themselves as 'Gods Chosen' and speak of the Old Testament prophets as 'Our Forefathers'. This naturally leads us to ask whether or not any of them were ethnic Jews? Considering that Eusebius records the first fifteen Bishops of Jerusalem as 'being of the circumcision' it would be strange if none of the apostolic fathers were of that ethnicity.
Were any of the Apostolic Fathers Jews?

The short answer is yes!

St. Ignatius of Antioch 

It is piously believed by many Catholics that St. Ignatius of Antioch was of Jewish origin. In fact, there is an ancient tradition that he was the child whom Christ took and presented to the apostles as the example of the one who is greater in the kingdom of heaven (Matt. 18:1-4).


  St. Ignatius of Antioch, the child who is greater in the kingdom of heaven 
  
  At that hour the disciples came to Jesus, saying: Who thinkest thou is the greater in the kingdom of heaven? And Jesus calling unto him a little child, set him in the midst of them, And said: Amen I say to you, unless you be converted, and become as little children, you shall not enter into the kingdom of heaven. Whosoever therefore shall humble himself as this little child, he is the greater in the kingdom of heaven. (Matthew 18:1-4)
  
  According to an ancient tradition, St. Ignatius of Antioch was the child whom Christ took and presented to the apostles as the example of the one who is greater in the kingdom of heaven. From that day the child, who was most beloved by the Savior and favored with the divine embrace, was also marked as the one upon whom lions would feast in the Roman Colosseum.


The Orthodox Church seem to piously hold to this tradition about St. Ignatius of Antioch also.

St. Barnabas

St. Barnabas was is considered an Apostolic Father and Barnabas was a Cypriot Jew. 


  Barnabas, born Joseph, was according to tradition an early Christian, one of the prominent Christian disciples in Jerusalem. According to Acts 4:36, Barnabas was a Cypriot Jew. Named an apostle in Acts 14:14, he and Paul the Apostle undertook missionary journeys together and defended Gentile converts against the Judaizers. They traveled together making more converts (c. 45–47), and participated in the Council of Jerusalem (c. 50). Barnabas and Paul successfully evangelized among the "God-fearing" Gentiles who attended synagogues in various Hellenized cities of Anatolia.
  
  Barnabas' story appears in the Acts of the Apostles, and Paul mentions him in some of his epistles. Tertullian named him as the author of the Epistle to the Hebrews, but this and other attributions are conjecture. Clement of Alexandria and some scholars have ascribed the Epistle of Barnabas to him, but his authorship is disputed.
  
  Although the date, place, and circumstances of his death are historically unverifiable, Christian tradition holds that Barnabas was martyred at Salamis, Cyprus, in 61 AD. He is traditionally identified as the founder of the Cypriot Orthodox Church. The feast day of Barnabas is celebrated on June 11. - Barnabas