The old-fashioned word was charge - i.e. my charge has now come of age.
From OED sense 14.
a. A thing or person entrusted to the care or management of any one.
spec. The people or district committed to the care of a minister of
1609 Shakespeare Troilus & Cressida v. ii. 7 Dio. How now my
charge. Cres. Now my sweet gardian.
Having submitted this answer earlier, I am now persuaded that ward is the better word and have up-voted @Kate Bunting's answer.
I no longer think foster son/daughter is correct, since, in the UK anyway, a foster-parent is not the same thing as a guardian. Though one must have regard to the OP's question which refers to guardian/custodian. A foster-parent is more of the nature of a custodian, with day to day control of the child's welfare, but usually under the supervision of a Local Authority, who hold the care order from the Court. It is the Authority who have legal guardianship.