Who else would it apply to, the infant?
what's the first phrase doing there at all, if it's only going to be overridden later in the same sentence?
Adults born in the colony
It's basic english as well as a rule of construction.
No, it would apply to "all who shall hereafter migrate into the same." So you are claiming that "all white persons born within the territory of this commonwealth" had to "give satisfactory proof by their own oath or affirmation, that they intend to reside therein, and moreover shall give assurance of fidelity to the commonwealth" in order to be citizens? At what age did they take those oaths? Do you have any historical evidence of Virginians actually doing that?
Adults born in the colony
Are you saying that the initial "all white persons born within the territory of this commonwealth" refers only to people already born, not to those who would be born later?