Virgil's Aeneid deals with the fate of Aeneas after the fall of Troy. Book 1 is a key place to look to determine the relationship between fate (Latin fatum) and the gods.
In Aeneid 1, Venus, after seeing Aeneas shipwrecked on the coast of northern Africa, namely Carthage, asks her father Jupiter whether he has changed his mind about what will ultimately happen to Aeneas and the surviving Trojans. Venus had understood that the following would take place:
Surely you promised that at some point, as the years rolled by,
the Romans would rise from them, leaders would rise,
restored from Teucer’s blood, who would hold power
over the sea, and all the lands. (A.S. Kline translation)
It seems to me that Venus' statement implies that Jupiter had the power to change Aeneas' fate.
Jupiter, in turn, responds that nothing has changed and that "your child’s fate remains unaltered." He says that Venus will still see come to pass all the things that "I promised".
So, from these passages it appears that, in theory, Jupiter had the power to alter a person's fate, but that he does not do so.
From Jupiter's speech here in Aeneid 1, we also have the image of fate being written down in a scroll ("unroll the secret scroll of destiny") and we get the impression that Jupiter has access to that scroll.
Thus, just as in modern times we have a person who is the executor of another person's last will and testament, we might compare Jupiter to the executor of a will, which has been decreed by fate. Even though, in theory Jupiter could alter what has been decreed, he will not do so.