Has there ever been evidence to prove that Caesarion was the son of Caesar?

There's not really much way to know one way or another, though I (and to my knowledge most, though not all, classicists) am inclined to believe that Caesarion really was Caesar's son. Caesar arrived in Egypt in October of 48 and Caesarion was born on June 23 of 47. In other words, while Caesarion was conceived sometime after Caesar arrived in Egypt they would've had to be real fast. That doesn't necessarily make it suspect, since we know that very soon after Caesar got to Alexandria he and Cleopatra began their affair, but it also makes it a bit too good to be true maybe. It's hard to believe who else might have been the father, however. It can't have been Ptolemy XIII, as Cleopatra had been driven out of Egypt early in 48 and was in open hostility against Ptolemy. Cleopatra's second husband Ptolemy XIV is equally unlikely, as he did not become her co-regent until January 47 and he was only 13 at the time.

Thing is, Caesarion's parentage only came under discussion following Caesar's death. Antony, during his maneuvers against Octavian following Caesar's death, insisted that Caesarion was Caesar's actual son, and Cassius Dio says that when Antony's will was read aloud (illegally) it named Caesarion Caesar's heir. Famously Suetonius says that Gaius Oppius wrote a pamphlet in which he proved that Caesarion could not possibly have been Caesar's son, although the contents are of course lost (and it's hard to believe that the argument relied more on logic than invective and rhetoric). Our sources are pretty divided on the issue. Cassius Dio asserts bluntly that Cleopatra was a liar, but what the hell did Cassius Dio know? Plutarch is inclined to believe that Caesarion was Caesar's son, but ultimately that's just his opinion. Only Suetonius gives some reason to think that perhaps Antony's claim wasn't just for political points (although it never would've been made had he thought that he couldn't score some):

quam denique accitam in urbem non nisi maximis honoribus praemiisque auctam remisit filiumque natum appellare nomine suo passus est. Quem quidem nonnulli Graecorum similem quoque Caesari et forma et incessu tradiderunt.

Later he brought her into the city and only sent her back when she was loaded with the greatest honors and gifts and allowed her to call her son by his name. Indeed this boy some of the Greeks have said was like Caesar in form and walk

That's not really too much to go on. Notice that Suetonius does not openly say that Caesarion was Caesar's son--even in Suetonius' lifetime it's doubtful whether such an assertion would've been acceptable. Even this, though, is not really sufficient evidence, as in the next sentence Suetonius says that Antony declared that Caesar had openly acknowledged Caesarion as his son, which makes it unclear whether Suetonius is getting his information that Caesar recognized Caesarion from Antony's speech or from other sources.

In short, the balance of opinion is probably, with a question mark. Nobody mentions the child before Caesar's death--Cicero, for example, is totally silent about the subject of a child when he mentions Cleopatra. So everything that we have is being filtered through post-Augustan suppression of the idea that Caesarion was Caesar's son. It's unlikely that anybody knew except for Cleopatra herself, and even then who knows whether she really knew who the father was, it's not like we know whom she was sleeping with at the time to check whether Caesar was the only reasonable option. Whether Caesarion's parentage was of actual significance is pretty debatable. His supposed relationship to Caesar was purely a political tool--nobody actually gave a shit except in that it weakened or strengthened various political positions. And Caesarion could never have been considered a legitimate child, since Caesar and Cleopatra were of course not married (and could not legally have been) and the idea of a foreign prince inheriting was beyond distasteful to a Roman, even one as unorthodox as Caesar