The term child as used in the regulations in this part includes:

(a) A legitimate child;

(b) A child legally adopted;

(c) A stepchild if a member of the veteran's household at the time of the death of the veteran, or

(d) An illegitimate child but as to the father only if acknowledged in writing signed by him, or if he has been judicially ordered or decreed to contribute to such child's support or has been judicially decreed to be the putative father of such child.