Heresies of the Patriarchs

A list showing the heretical patriarchs of four of the Apostolic sees; Rome (the pope is bishop of Rome, patriarch of the Latin Church, and Supreme Pontiff of the Catholic Church), Antioch, Alexandria, and Constantinople (which wasn't founded by an apostle, but made second in honor after Rome).1

Heresies: AR = Arianism, MP = Monophysitism, MT = Monothelitism, NE = Nestoriansim

Rome

Antioch

Alexandria

Constantinople

Silvester I 314

Eustathius 328

Athanasius 328

Alexander 317

Paulinas 330 (AR)

Eulalias 330 (AR)

Euphronius 332 (AR)

Mark 336

Flaccillus 335 (AR)

Julius I 337

Paul I 337

Eusebius 339 (AR)

Stephen I 343 (AR)

Macedonius 342 (AR)

Liberius 352

Leontius 344 (AR)

Eudoxius 358 (AR)

Ammonius 359 (AR)

Damasus I 366

Meletius 321

Eudoxius 360 (AR)

Paulinas 362

Evagrius 370

Demophilus 370 (AR)

Peter II 373

Gregory 379

Siricius 384

Flavian I 381

Timothy I 381

Nectarius 381

Evagrius 388

Theophilus 385

Anastasius I 399

Flavian I 393

John IC 398

Innocent I 401

Porphyrius 404

Arsacius 404

Alexander 413

Cyril 412

Atticus 406

Zosimus 417

Theodotus 417

Boniface I 418

Sisinnius I 426

Celestine I 422

John I 428

Nestorius 428 (NE)

Sixtus III 432

Maximian 431

Leo I 440

Domnus 441

Dioscorus I 444 (MP)

Proclus

Maximus 449

Flavian 446

Basil I 456

Proterius 452

Anatolius 449

Acacius 458

Timothy III 460

Gennadios 458

Hilary 461

Martyrius 460

Simplicius 468

Julian 471

Acacius 471

John IIC 477

Stephen II 478

Felix II 483

Calendion 481

John IT 482

Fravitas 489

Gelasius I 492

Palladius 488 (MP)

Euphemius 490

Anastasius II 496

Flavian II 498

John IIH 497 (MP)

Macedonius II 496

Symmachus 498

Severus 512 (MP)

John IIIN 505 (MP)

Timothy I 511 (MP)

Hormisdas 514

Dioscorus II 515 (MP)

Paul II 519

Timothy IV 519 (MP)

John IIC 518

John I

Euphrasius 521

Epiphanius 520

Felix III 526

Ephraem 526

Boniface II 530

John II 533

Agapitus I 535

Anthimius 535 (MP)

Silverius 536

Theodosius I 536 (MP)

Mennas 536

Vigilius 538

Domnus III 545

Paul C 538

Zolius 542

Pelagius I 556

Anastasius I 559

Apollinaris 551

Eutychius 552

John III 561

Gregory 570

John IVP 570

John IIIS 565

Benedict I 575

Eutychius 578

Pelagius II 579

Eulogius 581

John IVF 582

Gregory I 590

Anastasius I 593

Cyriacus 595

Sabinian 604

Anastasius II 599

Boniface III 607

Theodore S 607

Thomas I 607

Boniface IV 608

Athanasius 611 (MP)

John VA 609

Sergius I 610 (MT)

Adeodatus I 615

Boniface V 619

George 620

Honorius I 625*

John II 631 (MT)

Cyrus P 631 (MT)

Pyrrus 639 (MT)

Severinus 640

John IV 640

Paul II 641 (MT)

Theodore I 642

Martin I 649

Eugenius I 655

Among the Patriarchs of Jerusalem, St. Cyril of Jerusalem (Semi-Arian until A.D. 380), Juvenal (Monophysite), Theodosius (Monophysite) and Martyrius (Monophysite) were heretics.

St. Maximus the Confessor:
The extremities of the earth, and everyone in every part of it who purely and rightly confess the Lord, look directly towards the Most Holy Roman Church and her confession and faith, as to a sun of unfailing light awaiting from her the brilliant radiance of the sacred dogmas of our Fathers, according to that which the inspired and holy Councils have stainlessly and piously decreed. For, from the descent of the Incarnate Word amongst us, all the churches in every part of the world have held the greatest Church alone to be their base and foundation, seeing that, according to the promise of Christ Our Savior, the gates of hell will never prevail against her, that she has the keys of the orthodox confession and right faith in Him, that she opens the true and exclusive religion to such men as approach with piety, and she shuts up and locks every heretical mouth which speaks against the Most High. (Opuscula theologica et polemica).

Source:Born Fundamentalist, Born Again Catholic by David Currie, though he says he took it from the History of Christendom series by Warren H Carrol.

Honorius was condemned by the sixth ecumenical council not for heresy, but for failing to declare ex cathedra the Catholic faith on the dispute at hand, as Pope Leo II's confirmation of the Council says when he states: "We anathematize the inventors of the new error, that is, Theodore, Sergius,...and also Honorius, who did not attempt to sanctify this Apostolic Church with the teaching of Apostolic tradition, but by profane treachery permitted its purity to be polluted."
Taken from the original Heresies of the Patriarchs on the wayback machine.