Cleopatra and Caesar's son Caesar Jr. can enjoy the friendship with Rome?

The principle of ancient Roman civil law: the identity of children is determined by the identity of fathers. Caesar is a citizen of ancient Rome, so his son can become a Roman citizen. But Cleopatra can't. She is an Egyptian, not a Roman, but a person from a conquered area. She can't be a Roman citizen, so she can't be a Roman citizen.

Believe me, I majored in history and just learned the Roman law system.