Checklist of First Century works:
30-160 New Testament
80-120 Epistle of Barnabas (Clement Alexandrine & Origen used it, Jerome considered its authorship genuine & Eusebius didn't, Vulgate used it as apocryphal)
80-140 1 Clement
90-218 4 Esdras (Vulgate) / 2 Esdras (Protestant) / 3 Esdras (Slavic) including Chp 7 w/ NSRV verses 35-105
100-150 Apocalypse of Peter (Most of it extant. Muratorian canon has it but says some ban it from reading in church, Accepted by Clement Alexandrine, not counted genuine by Eusebius)
100-160 Shepherd of Hermas (included in Codex Sinaiticus; Muratorian fragment says it "ought indeed to be read; but it cannot be read publicly"; Clement Alexandrine uses it but notes "many people despise it")
Fragmentary, or Acceptance Uncertain or Varied (ie. I am not sure what their status has been)
70-120 Egerton Gospel (could be fragments from a rejected gospel that we only have in fragments like g.Peter)
70-200 Fayyum Fragment (too short to tell what writing it belongs to)
80-150 Gospel of the Hebrews (Fragments. Used by Origen, Jerome, Didymus Blind, Papias, Hegesippus; rejected by Pseudo-Cyril Jerusalemite & Philip Sidetes as heretical)
100-150 Preaching of Peter (Fragmentary. Accepted by Clement Alexandrine, not counted as genuine by Eusebius)
100-160 Gospel/Traditions of Matthias (what date is right? EW site says 110-160, but backup would be good.)
100-420 Gospel of Bartholomew, The Questions of Bartholomew, "Resurrection of Jesus Christ" by Bartholomew (possibly the same work. Accepted by anyone? Rejected by Jerome. What date is best?)
Likely Christian influenced works about the OT period but not in Biblical apocryphas.
Early 1st to late 5th c. Lives of the Prophets
1st to 2nd c. Testament of Abraham
1st to early 3rd c. Martyrdom and Ascension of Isaiah http://www.earlyjewishwritings.com/ascensionisaiah.html
1st c. to 300 Apocalypse of Elijah http://www.earlyjewishwritings.com/apocelijah.html
1st c. - 300 3 Baruch
1st c. -300 4 Baruch http://www.earlyjewishwritings.com/4baruch.html
70-200 Testaments of the Twelve Patriarchs
100-200 Odes of Solomon
2nd-3rd c. Testament of Jacob http://www.earlyjewishwritings.com/testjacob.html
100-400 Testament of Isaac http://www.earlyjewishwritings.com/testisaac.html
100-400 Testament of Adam http://www.earlyjewishwritings.com/testadam.html
100-400 Hellenistic Synagogal Prayers (found in James H. Charlesworth, ed., “Hellenistic Synagogal Prayers,” The Old Testament Pseudepigrapha)
100-500 Apocalypse of Sedrach http://www.earlyjewishwritings.com/apocsedrach.html
100-900 Greek Apocalypse of Ezra
100-150 Apocryphon(Secret Book) of James (Nag Hammadi. Work supports James & Peter but dissents from other disciples. Cerinthian? Cerinthus the gnost required Torah observance & conflicted w St.John who was 1 of 3 church pillars)
100-160 Gospel of the Nazarenes/Nazoreans (Torah-observant, theologically orthodox Christian Nazarene sect; Jerome used it; 7th c. Trullo council banned Christians from praying in synagogues)
100-160 Gospel of the Ebionites (Is it gnostic?)
Celibate / Encratitic?
80-150 Gospel of the Egyptians (Clement Alexandrine quoted it as having real Jesus sayings, Origen called it heretical)
Docetist (eg. Jesus only appeared to suffer)
50-140 Oxyrhynchus 1224 Gospel [maybe the Gospel of Peter]
70-160 Gospel of Peter (Ever accepted? Rejected by Serapion Antiochene & Philip Sidetes)
50-140 Gospel of Thomas (was the Greek one gnostic? Is it Matthew/Matthai's sayings gospel?)
50-150 Apocalypse of Adam (gnostic, Nag Hammadi. Is it Christian?)
50-150 Eugnostos the Blessed (Nag Hammadi)
50-200 Sophia of Jesus Christ (Nag Hammadi)
80-250 Christian Sibyllines
100-200 Gospel of Eve
100-230 Thunder, Perfect Mind
100-300 Coptic Apocalypse of Peter / "Gnostic Apocalypse of Peter"(Wikipedia dates it to 100-200 AD. What dating is best?)
NonChristian Jews writing on Christianity
93 Flavius Josephus
70 - 100 Birkat Ha Minim by Shmuel ha-Katan
Pagans writing on Christianity
Pliny the Elder 23-79 AD (remarks about the tetrarchy of the Nazareans)
Phlegon (on the eclipse http://www.textexcavation.com/testimonia.html)
Thallus (on the eclipse http://www.textexcavation.com/thallustestimonium.html)
Seneca on Anger http://www.textexcavation.com/seneca.html (maybe not about Jesus?)
73-200 Mara Bar Serapion
Likely modern forgeries
70-1973 Secret Mark
Entries in bold I researched and read in connection with this thread
Entries in red I would add to the Early Christian Writings list (Most of them are already in the Jewish writings section)
(For Christian writings about the OT period, consider 1. Ascertain dating. 2. Christian authorship vs. interpolations)
*Eusebius on Preaching of Peter, https://www.ccel.org/ccel/schaff/npnf20 ... i.iii.html ; on his classification of books, http://www.ntcanon.org/Eusebius.shtml
Church figures, besides the Bible's ascribed authors, who reached adulthood in the 1st c. AD:
P.Clement of Rome (s. 99 AD)
Bp. Ignatius Antiochene (35-108)
Bp. Dionysius the Areopagite, 1st. Bp of Athens (some pseudographical writings were ascribed to him some centuries later)
Quadratus of Athens (-129), wrote an "Apologia" to Hadrian c.124-125
Aristides of Athens ( -134)
Cerinthus (gnostic opponent of St. John active in c. 100)
Am I missing any?
Major 2nd c. figures:
Justin Martyr (100-165)
Athenagoras of Athens (133-190)
Melito of Sardis (-180)
Theophilus of Antioch (-180s)
P.Victor of Rome (-199) notable for Quartodeciman controversy
Clement of Alexandria (150-215)
Tertullian (155 – c. 240)
The bishops of Antioch after Peter were Evodius (d.66 AD) and Ignatius(lived 35-108). Not much seems written of Evodius. https://en.wikipedia.org/wiki/Evodius
Rome's popes after Peter were Linus (d.76 AD), Anacletus/Cletus (d.92), Clement (d.99), Evaristus/Aristus (d. 107)
Clement was author of 1 Clement. Not much seems written of the authors. (See eg. https://en.wikipedia.org/wiki/Pope_Linus)
Alexandria's Patriarchs were: Mark the Evangelist (d.68), Ananius (d.83), Avilius (d.95), Kedron (d. 106)
(https://en.wikipedia.org/wiki/Pope_Ania ... Alexandria , https://en.wikipedia.org/wiki/Pope_Avil ... Alexandria)
Jerusalem's Patriarch after James' death in c.62-70 AD was Simeon I (.d 107 or 117). There is confusion over which and how many bishops Jerusalem had between then and the Bar Kokhba revolt of 135 AD, since the bishops listed could have been serving concurrently in that church. (https://en.wikipedia.org/wiki/Simeon_of_Jerusalem)
The first bishop of Athens is sometimes listed as Hierotheos the Thesmothete, after whom came Dionysius the Areopagite (d. c.96), after which there was no bp until 117.
The bishop of Gaul before Ireneus was Pothinus (~87 AD - ~177 AD) (https://en.wikipedia.org/wiki/Saint_Pothinus)
I can't find a list of bishops for Damascus, except that maybe Ananius was one. He met Paul in Acts, and I wonder if he is the person who with his wife died later after Peter denounced them (although that would seem unlikely considering the place of honor Acts otherwise gives him). (https://en.wikipedia.org/wiki/Ananias_of_Damascus)
For Corinth, Saint Apollo of Ephesus AKA Apollos (mentioned in the NT) is considered the first bishop. Others sometimes considered to be 1st c. bishops are Silas, Onesiphorus, Sosthenes.
For Ephesus, St. Timothy, Onesimus (.d c. AD 68), Gaius (d.97) are considered the first c. bishops.
In Libya, Lucius of Cyrene is considered the first bishop. This could be St. Luke. https://en.wikipedia.org/wiki/Lucius_of_Cyrene
For Crete, Titus is considered the first bishop (died 96 or 107)
For Caesarea, Zaccheus (the publican in the NT) is considered the first bishop.
In Pannonia (northern Yugoslavia, west Hungary), Andronicus preached, but there are not many records.
The bishop of Malta was Publius, who was transferred to Athens in 90 and d. 125.
For Edessa, there are apocryphal stories about Thaddeus, King Abgar, and the Mandylion (maybe Turin shroud).
For Britain, stories about Joseph of Arimathea are apocryphal.
For India, there are stories about Thomas, which have some credibility, as Christianity seems planted there already in the 2nd-3rd c.
For Cyprus and Provence (France) there are stories that Lazarus (from the NT) became a 1st c. bishop. (https://en.wikipedia.org/wiki/Lazarus_of_Bethany). Another is that Barnabas founded the church there.
For Galatia, Crescens is considered a 1st c. bishop in the 4th c. Apostolic Constitutions.
For Carthage, Crescens or Epenetus of Carthage could the first c. bishop.
There is so little written by or about these 1st c. figures that comes from the 1st to 2nd c. AD. But we know that they played a big role in establishing a serious religious community across the Mediterranean.