If he isn't the son of Ceasar than whose is he? Titus Pullo?
No, I am not alluding to anything like that. My goal was to emphasise the fact that Caesar never really paid much attention to Caesarion - at least IOTL- and that the fact that he was Caesar's son was primarily promoted by Mark Antony for political reasons. Although I agree that Caesarion was too young when Caesar died, I don't think that Caesar would have any plans of introducing Caesarion to Roman political life : Octavian would be his main heir and political successor in Rome.
This however doesn't mean that Caesar wouldn't have any plans for Caesarion. In fact, it could be argued perhaps that the latter could become an important part of Caesar's eastern policy : more specifically, that Caesar might envision Caesarion to become
his successor in the East.
By that I mean that Caesar could potentially end up considering Caesarion as the solution to Rome's eastern problems: as a member of the Ptolemaic and Seleucid dynasties, he would be seen as a legitimate ruler in Asia, if he were for example to become king of the kingdom I described in my first post on the thread. But he would also be closely related to Rome, through the citizenship he would most likely obtain, as well as the fact that, as Caesar's son, he would have ties to one of Rome's most ancient and noble families. Therefore, he could become Rome's lieutenant in the East, with the former retaining most probably the three Anatolian provinces - Asia, Bithynia et Pontus and western part of Cilicia (Pisidia, Pamphylia, Milyas) and direct overlordship over the various client kingdoms of Asia Minor, while Caesarion would become king of Syria, Cilicia, Mesopotamia, Babylonia and Susiana, which in turn would form a strong counterweight to Parthia that would have close ties with Rome. The result of such an arrangement would be (at least in theory) that the East would remain in the Roman sphere of influence, while the Republic wouldn't have to bear the burden of military and civil maintenance in those regions, as well as take on the arduous task of integration. I agree that this is probably too revolutionary an idea, but at the same time, I don't think that it would be beyond Caesar to conceive such a plan; and given that the Donations of Alexandria and a whole bunch of other things still weren't enough for Octavian to get his way with Antony easily, I think that Caesar, with his prestige and influence, could potentially get this done - or it could lead to his downfall.