<< For non-Catholics: Who are these 44 ECF that did not hold Peter was the Rock? And where did they say this? >>
The folks who cite this are getting their information from an old James White debate on the Papacy (with Matatics, or with Fr. Pacwa) or article or White’s book (The Roman Catholic Controversy), or from the source White got this from, a secondary anti-Catholic source: George Salmon’s Infallibility of the Church who is citing a study from the 19th century (Maldonatus, or Launoy a “Gallican”) that used “Fathers” and “Doctors” right through the Reformation and Renaissance. So we’re not talking exactly “patristic writers” which the Anglican Salmon mistakenly alleges.
Here is the precise source this is taken from, bingo found it
(3) The most elaborate examination of the opinions of the Fathers is in an Epistle [Epistle vii., Opp. vol. v., pt. 2. p. 99: Geneva, 1731] by the French Roman Catholic Launoy, in which, besides the interpretation that Peter was the rock, for which he produces seventeen Patristic testimonies, he gives the interpretations that the rock was the faith which Peter confessed, supported by forty-four quotations; that the rock was Christ Himself, supported by sixteen; and that the Church was built on all the Apostles, supported by eight.
(4) The Jesuit Maldonatus, whose Romanism is of the most thorough-going kind, begins his commentary on this passage by saying, “There are among ancient authors some who interpret ‘on this rock,’ that is, ‘on this faith,’ or ‘on this confession of faith in which thou hast called me the Son of the living God,’ as Hilary, and Gregory Nyssen, and Chrysostom, and Cyril of Alexandria. St. Augustine going still further away from the true sense interprets ‘on this rock,’ that is, ‘on myself Christ,’ because Christ was the rock. But Origen ‘on this rock,’ on all men who have the same faith.” 
Found here bible.ca/cath-salmon-infallibility.htm
That’s the source for the numbers and “Fathers” – the anti-Catholic Anglican Salmon. Now B.C. Butler in his response looked up the original study and shows the “Fathers” or “patristic writers” include Catholic writers from the Reformation or Renaisance period who obviously fully accepted the Papacy, so it matters little how they interpreted Matthew 16:18 at that point.
It demonstrates nothing since we’re not talking pre-500 AD Fathers. All the earliest Fathers (i.e. pre-500 AD) said without exception Peter was the Rock, or his faith was Rock, or both. Wanted to add: In Augustine you can find four interpretations: Peter, Peter’s faith, Peter’s successors, and Christ. And the same in the Catechism of the Catholic Church: (a copy/paste here)
The literal interpretation is that Simon alone is the rock of Christ’s Church, the Church is built on Peter personally (CCC 881, 586, 552). However, the Catechism also notes that Peter is the unshakeable rock because of his faith in Christ (CCC 552); that the acknowledgement of Christ’s divine sonship is the Church’s foundation (CCC 442); on the rock of Peter’s faith Christ built His Church (CCC 424); and Christ Himself as rock and “chief cornerstone” (1 Peter 2:4ff; 1 Cor 10:4; Eph 2:20) is the foundation (CCC 756). Many of these views can be found in the early Church Fathers as Catholic convert Stephen Ray (Upon This Rock) and former Catholic William Webster (The Matthew 16 Controversy) have pointed out in their books and online debates.
Here is an exhaustive study by John Chapman on St. John Chrysostom the great eastern Father, who said both Peter = Rock and his faith = rock, and was very clear about the jurisdictional primacy of Peter.
You should also check out Steve Ray’s reply to Bill Webster from a number of years ago, available as Word .doc files, they discuss all the major early Fathers (pre-500 AD) in depth.