Methodology for Cataloging New Testament Quotes by early Christians up to to 325 A.D.
Sorting note: You can take the Excel spreadsheet, and sort it by the Index, and it will give you the breakdowns by each book.
1. What time period does this cover? These cover the first known extra-Biblical writer, Clement of Rome (writiing 96 or 98 A.D.) to just past the First Council of Nicea, with Alexander of Alexandria (313-326 A.D.)
2. Which authors are included?
I included all early church writings (including Tertullian and Novatian, and Tatian's Diatessaron, up to 326 A.D. I did not Tatian's other writing, Gnostics, Ebionites, or Bardasenes.
Here is what I included in chronological order.
Clement of Rome 96 or 98 A.D. Origen (heterodox teacher) 225-253/254 A.D.
Papias of Hierapolis, disciple of John 95-110 A.D. Novatian (his schism lasted over 200 years) 250/254-257 A.D.
Presbyters (Papias?) -95-117 A.D. Treatise Against Novatian 254-256 A.D.
Ignatius, disciple of John. (shorter Greek version) c.100-117 A.D. Treatise on Rebaptism c.250-258 A.D.
The Didache (= Teaching of the Twelve Apostles) before 125 A.D. Cyprian of Carthage (against Novatian) c.246-258 A.D.
Apology of Aristides (Greek version) 125 or 138-161 A.D. No New Testament quotes Roman church leaders (letters 2,29,30) 250-251 A.D.
Quadratus of Athens fragment (apologist) 126 A.D. Lucian et al. (letters 16, 21) 250-251 A.D.
Letter to Diognesus (=Mathetes to Diognetes) c.130 A.D. Caldonius to Cyprian (letter 18) 250-251 A.D.
Epistle of Barnabas 100-150 A.D. Celerinus to Lucian (letter 20) 250-251 A.D.
2 Clement (anonymous writer) c.150 A.D. Moyses, et al. to Cyprian (letter 25) 250 A.D.
Polycarp's Epistle to the Philippians 100-155 A.D. Cornelius to Cyprian (letters 45,47) c246-256 A.D.
The Shepherd of Hermas c.160 A.D. Maximus, et al. to Cyprian (letter 49) c246-256 A.D.
Justin Martyr, philosopher and apologist c.138-165 A.D. Firmilian of Caesarea to Cyprian (letter74) 256 A.D.
Everestus' Martyrdom of Polycarp c.169 A.D. Nemesianus, et al. to Cyprian (letter77) 254-257 A.D.
Dionysius of Corinth (wrote against Marcion) 170 A.D. Lucius and the brethren to Cyprian (letter78) 254-257 A.D.
Tatian's Diatessaron died 172 A.D. Felix & the rest of the martyrs to Cyprian (79) 254-257 A.D.
Christians of Vienna and Lugdunum (Lyons) 177 A.D. Seventh Council of Carthage (85 bishops)  258 A.D.
Athenagoras (apologist) 177 A.D. Pontius’ The Life and Passion of Cyprian 258 A.D. No New Testament quotes
Melito/Meleto of Sardis (Quartodecimian) 170-177 A.D. Theognostus of Alexandria (Origenist) 260 A.D. No New Testament quotes
Claudius Apollinaris of Hierapolis 160-177/180 A.D. Gregory Thaumaturgus (undisputed works) 240-265 A.D.
Hegesippus (chronicler) 170-180 A.D. Dionysius of Alexandria (Origenist) 246-265 A.D.
Rhodon (against Marcion and Apelles) 180 A.D. Dionysius of Rome (Against the Sabellians) 259-269 A.D.
Theophilus of Caesarea 180 A.D. Malchion (Against Paul of Samosata) 270 A.D. No New Testament quotes
Theophilus of Antioch (to Autolycus) 168-181/188 A.D. Pierius of Alexandria (fragment) 275 A.D.
Irenaeus of Lyons, disciple of Polycarp c.160-202 A.D. Anatolius of Alexandria (mathematician) 270-280 A.D.
Maximus of Jerusalem (wrote on origin of evil) 185-196 A.D. Theonas of Alexandria (Letter to Lucianus) 282-300 A.D.
Polycrates of Ephesus (Quartodecimian) 196 A.D. Adamantius Dialog on the True Faith in God c.300 A.D.
Passion of the Scillitan Martyrs -died 180 A.D. 180-202 A.D. Alexander of Lycopolis Of the Manichaeans 301 A.D. No New Testament quotes
Caius and the Muratorian Canon 190-217 A.D. Arnobius Against the Heathen (undisputed) 297-303 A.D. No New Testament quotes
Passion of Perpetua and Felicitas c.201/205 A.D. Victorinus of Petau, Austria -commentator martyred 304 A.D.
Epitaph of Abercius of Hieropolis in Phrygia Salutaris 190-210 A.D. Council of Elvira (21 undisputed canons) 306/307 A.D.
Serapion of Antioch (against Marcion) 191/200-210 A.D. Phileas of Thmuis/Tmai, Egyptian Delta beheaded 307 A.D.
Minucius Felix (The Octavius) 210 A.D. Pamphilus disciple of Pierius (Origenist) martyred 309 A.D. No New Testament quotes
Apollonius of Ephesus (against Montanists) c.210 A.D. Creed of Lucian of Antioch c.300-311 A.D.
Clement of Alexandria 193-217/220 A.D. Peter of Alexandria (undisputed) 306,285-311 A.D.
Tertullian (joined the Montanist Church) 198-220 A.D. Methodius (corrected Origen’s followers) 270-311/312 A.D.
Asterius Urbanus (against Montanists) c.232 A.D. No New Testament quotes Council of Ancyra (about 12 bishops) 314 A.D.
Hippolytus, pupil of Irenaeus (undisputed) 222-235/236 A.D. Council of Arles, southern France 314 A.D. No New Testament quotes
Narrative of Zosimus before 240 A.D. No New Testament quotes Council of Neocaesarea (Basil and others) c.315 A.D.
Instructions of Commodianus c.240 A.D. Martyrdom of Habib the Deacon by Theophilus events c.315 A.D.
Julius Africanus (undisputed writings) 232-245 A.D. Athanasius Against the Heathen & Incarnation c.318 A.D.
Martyrdom of the Holy Martyrs before 250 A.D. No New Testament quotes Lactantius c.303-320/325 A.D.
Acts of Xanthippe, Polyxena, and Rebecca perhaps mid 3rd century No New Testament quotes Alexander of Alexandria 313-326 A.D.0 No New Testament quotes
Alexander of Cappadocia (Clem. A’.s pupil)  233-251 A.D. No New Testament quotes Eusebius of Caesarea 318-325 A.D.
3. Why do I count fractions of verses? The early writers felt no compulsion to start and stop quotes at particular verses as we number them. Verses were not numbered until the thirteenth century, so you have to count fractions of verses to be more precise.
4. How do I count fractions of verses?
Here is an example: let’s say a writer quoted a middle 1/4 of a verse, or even if four or five writers quoted the same middle 1/4 of a verse.
So to keep track of partial verses, after a quote I put “(full quote)”, or for example 4:15a (1/4 quote) if they quoted the first 1/4 quote of 4:15, or 4:15f (1/5 quote) if they quoted that last 4/5 of the verse.
However, in cases where one or more writers already covered the entire verse, additional writers will not change the percentage quoted at all. 
So in some cases, especially in the gospels, I just put the very without differentiating how much they quoted. I could go back to do that later, but I put it at low priority since the verse was already covered.
5. How do I count the middle of verses?
Another issue is that saying the covered the middle 1/4 of a verse, such as 4:15m (1/4 quote), is not sufficient precision when combined with other quotes that also covered different parts of the verse. So I used the nomenclature such as
4:15m (not 3 4 not 9) meaning they did not quote the first 3 words, they quoted the next 4, and they did not quote the last 9 words.
Sometimes they quoted only the first and lat parts of a verse, or they otherwise quoted it with gaps, and I used the same nomenclature for that.
In some cases I still have the older method I used, 4:15m (1/4 quote), but only when I had the verse elsewhere covered. I plan to go back and update that too, but again, that is a lower priority since it will not affect the overall percentage.
6. How did I estimate fractions? 
I went by words in Greek or major words in English, not Greek letters.
In many cases I found the Greek words by using the Aland New Testament. However, some of the time I did not have that available so I estimated using English.  I found estimating gave similar ratios, such as one half vs. 5/11, and the errors of estimating too high or too low tended to cancel themselves out.
So there is a lot more work I could do if you wanted to get the exact percentage quoted for every single author, but what I currently have should be accurate for the overall percentage.
I looked at the words (in English) and if part was a quote and part was a paraphrase, I only counted that part where the words matched. In some cases though it was a quote that said something like “you” and the writer replaced it with “we”, or similar, and I counted that but noted it. References that are just allusions or paraphrases are not on the list at all.
In some cases I have not yet differentiated how much of a verse a particular writer quoted, if other writers have already quoted the entire verse.