Did John the Evangelist make a mistake in counting the post-resurrection apparitions of Jesus? We see Jesus making his post-resurrection apparition before the disciples on various occasions: first, to the disciples on their way to Emmaus (Lk 24: 13-35), second, to the disciples in the absence of Thomas (Jn 20:19) then in the presence of Thomas (Jn 20:26) followed by the apparition at Tiberius (Jn 21:1). John specifies the Tiberius apparition as the third one (Jn 21:14), whereas it should have stood at 4th place, counting from the Emmaus apparition.
My question therefore is: Did John the Evangelist make a mistake in counting in order, the post-resurrection apparitions of Jesus? What does the Catholic Church say about such a prospect?
I am unaware of any specific statement by the Catholic Church on this question.
It's possible that this could be interpreted as a mistake, but I think there's a simpler solution:
What is the inner circle of Jesus' closest disciples called?

In the Synoptics they are usually &quot;the twelve&quot;
Luke 6:13 is likely the earliest reference indicating that the twelve were also called &quot;apostles&quot;
John calls them &quot;disciples&quot;

So applying John's terminology consistently, I see John 21:14 calling out that this was the third appearance to the apostles as a group.
John himself acknowledges this wasn't the third appearance in the absolute sense--he records the appearance to Mary Magdalene, who certainly was a disciple in the general sense of the word; just not an apostle.
Putting the Gospels together, we have appearances to:

Mary Magdalene
Mary the mother of James &amp; Joses, Joanna, Salome (and possibly others)
Peter
Cleopas and his companion (could be before #3)
10 of the original apostles (Thomas absent, Judas absent and possibly dead), plus possibly others
11 of the original apostles (Thomas now present, Judas absent and probably dead)
The appearance at the Sea of Tiberius

(The timing of the appearance to James (aka James the Just) is unknown; this theory would suggest that the appearance to 500+ (as recorded by Paul in 1 Cor 15) probably happened after the appearance at the Sea of Tiberius)
I've bolded the appearances to the apostles as a group, and the Sea of Tiberius is indeed #3 on the list.