Another church, the Elmali Kilise, that is almost identical. It also has a boy in a tree, but is has more text.
To identify that I contacted a person I had corresponded with earlier. He is a priest and Graecist. As it was in Dutch I translate:
On the top edge it says Η ΒΑΙΝΟΦΟΡΟC, i.e. The (olive/palm) branch-bearing (feast/event). So it concerns Jesus' entry into Jerusalem, indicated by the open gate and walls. Three figures receive Him and speak to Him (see the “speaking” hands). Jesus himself also speaks; his two fingers do indicate his dual nature (God-man).
The figures in the tree are supposed to represent children. The Bible (New Testament) only mentions people spreading clothes on the ground and waving branches. But the text to the left of the tree tolerates no misunderstanding:
ΠΕΔΕΣ ΝΟΝ (?) ΕΒΡΕΟΝ i.e., Children of the Hebrews.
The boy against the trunk of the treed shouts up: [X?]EICENI – or: EICENI – or: CICENI KOΨE ME KΛAΔΗ.
Sisen(n)i(e), the choice of the latter, has the advantage that it concerns a name that was in vogue in the Byzantine Empire and in the even more eastward oriental churches, namely Sisinnios. That name was already known in the IV century and remained so in the East until the following centuries. For example, there is a deacon known from the IVth with that name and who came from Kappadokia (!!!) and even a pope from Syria. The name is of Persian origin, but I don't know what it means.

“Cut off (a few) branches,” the boy shouts, of course so he can wave with them.
Where did those children's ideas come from? Because the Bible text only talks about “the people, they... people...). But the ancient Roman liturgy has an antiphon, which reads: “Pueri Hebraeorum, portantes ramos olivarum, obviaverunt Domino, clamantes et dicentes: Hosanna in excelsis” i.e., the children of the Hebrews came to meet the Lord with olive branches, shouting with a loud voice, Hosanna in the highest. This antiphon is the most important in the liturgy of Palm Sunday (the Lord's entry into Jerusalem) and is still sung here and there in Latin. Enough reasons to adopt an ancient tradition in this regard.
Final comment: as in all explanatory texts on the frescoes in and around Göreme, these short texts are also teeming with spelling errors, interesting for a Graecist.”

That invalidates what I wrote earlier:

On a site of my own I was informed an attribution (Jesus entering Jerusalem) was wrong. In German it said: "This scene shows (from Luke 19:1-10) Jesus entering Jericho, where in a tree is Zacchaeus (Greek Ζακχαῖος, Hebrew זכי, which means pure)." The Wikipedia informs us: Zacchaeus [...] according to chapter 19 of the gospel of Luke, was a superintendent of customs; a chief tax-gatherer (Latin: publicanus) at Jericho (Luke 19:1-10). Tax collectors were hated by many of their fellow Jews, who saw them as traitors for working for the Roman Empire. Because the lucrative production and export of balsam was centered in Jericho, his position would have carried both importance and wealth. In the account, he arrived before the crowd who were later to meet with Jesus, who was passing through Jericho on his way to Jerusalem. Described as a short man, the Zacchaeus climbed up a sycamore fig tree so that he might be able to see Jesus. When Jesus reached the spot he looked up into the branches, addressed Zacchaeus by name, and told him to come down, for he intended to visit his house. The crowd was shocked that Christ would sully himself by being a guest of a tax collector. Moved by the audacity of Jesus's unconditional love and acceptance, Zacchaeus publicly repented of acts of corruption and vowed to make restitution for them, and held a feast at his house.