Ceasar was kidnapped by pirates in his early days, but there are varying accounts about this. Plutarch for example says that the pirates were later crucified and Sueton mentions that first their throats were cut, but I've wondered whether later historians in the byzantine time or the middle ages actually also wrote about this event, and if so, do we still have their writings? Are there even artistic portrayals in theater of the renaissance or something similar?
As far as I know, these are the sources regarding the capture of Caesar by pirates:
Velleius Paterculus.Roman History. 2.41.3
Valerius. Maximus. 6.9.15.
Plutarch. Caesar. 1.8-2.7.
Plutarch. Crassus. 7.5.
Plutarch. Moralia. 205E - 206A.
Suetonius. Caesar. 4.1-2, 74.1.
Polyaenus. Stratagems. 8.23.1
Pseudo-Aurelius Victor. The illustrious men of the city of Rome. 78.3.
Plutarch, as you have said, says that the pirates were crucified. Suetonius, actually says that the pirates were also crucified after having their throats cut(Suetonius. Caesar. 74.1):
Even in avenging wrongs he was by nature most merciful, and when he got hold of the pirates who had captured him, he had them crucified, since he had sworn beforehand that he would do so, but ordered that their throats be cut first.
The fact that Plutarch does not mention it may just be because it was not in the interest of him to do so. However, if you read the full section of Suetonius, his context is that he is trying to highlight examples of Caesar showing mercy, therefore it is in the interest of Suetonius to provide this extra detail in order to display the act of mercy. Whether or not it is actually true is unknown to us, but under the context of Suetonius you can see why he would include it if it is true, were as Plutarch would not.
Polyaenus offers a different version to both Plutarch and Suetonius (Polyaenus. Stratagems. 8.23.1):
Caesar then paid them the double sum, as he had promised; and made them partake of the banquet he had prepared. In high spirits at the large sum they had received, they gave loose to their appetite, and drank freely of the drugged wine, which presently sent them to sleep. In that state Caesar ordered them to be slain, and he immediately repaid the money to the Milesians.
Here you can see that it says that Caesar actually killed them upon the conclusion of a feast after drugging them rather than having them crucified once they were captured as commonly reported.
There has been scholarly articles that discuss Caesar and his capture by pirates because it was included within the work of so many contemporary authors - what was the purpose of including such a story? Some scholars try to argue that the episode is even written about because it foreshadows what Caesar will become in the future.
I would actually recommend this article available online here:
Osgood, J. (2010). 'Caesar and the Pirates: Or How to Make (and break) an Ancient Life'. Greece & Rome 57: 319-336
As far as I am aware, there is no later sources past the 4th century that mention or discuss the episode.