As far as I know Jesus was born around 1AD (+/- 3 years depends on a source ) but what was the year when he was born, before we started diving years between BC and AD? What would he have in his birth certificate?
Jesus would almost certainly not have had a birth certificate. Birth registration for Roman citizens was introduced by Augustus a decade or so before Jesus' birth, but it wasn't mandatory and applied only to Roman citizens, which Jesus was not. And there was no Jewish or Judean birth registration system.
If you're asking what he and his parents would have called the year in which he was born, the Judeans at that point mostly used Seleucid Era dating, so they would have said it was "308 since the rule of Alexander." The Romans, like Pilate, probably would have said it was "the year that C. Calvisius Sabinus and L. Passienus Rufus were consuls" if they were using the Roman system (that would be our 4 BCE, which is when most scholars think Jesus was born)