Good researchBen C. Smith wrote: 34.1 In the third year of the reign of the emperor mentioned above [= Trajan], ...
36.1 At that time Polycarp, a disciple of the apostles, was a man of eminence in Asia, having been entrusted with the episcopate of the church of Smyrna by those who had seen and heard the Lord. 2 And at the same time Papias, bishop of the parish of Hierapolis, became well known, as did also Ignatius, who was chosen bishop of Antioch, second in succession to Peter, and whose fame is still celebrated by a great many.
Trajan's third year should be about 101.
That seems to show - Polycarp a man of eminence (at age 32), Papias becoming well-known, and Ignatius becoming well-known - in 101.
Note Polycarp to Philippians is usually dated 110-140.
Ignatius' books maybe 107, more likely 130s.
Papias' words about proto-Gospels could date from 95 - 140.
Kapyong
(' books Added later for clarity.)