The Chasam Sofer ( Shu”t E.H. 76) discusses if an adopted son may be called up to the Torah as the son of his adoptive father.
We see from the Ramban’s Girsa in the Targum Unkelesthat Serach was the daughter of Osher’s wife and not of Osher.(SEE HERE)
The Torah still calls her Bas Osher.
The reason is, because, since he raised her, he is considered as the father. So too an adopted son can be called up as the son of his adoptive father.
On the other hand, Tosfos in Pesachim (54a), says
” We don’t find in the whole Torah , that a son of a wife
is called his son.”
The Knesess Hagedola holds, Tosfos is only where
the father has also biological sons.
The Chasam Sofer explains the reason is, because a person wants his Yerusha (inheritance) to go only to his own (biological) children. By calling him a son there is a danger he will end up inheriting together with his own children.
In a case where there are no children of his own, then he is called a son. (he probably wants the Yerushato go to him).
If they adopt a daughter, then even if the husbandhas sons of his own, being there is no danger of her inheriting with brothers, she is called a daughter.*
Therefore Serach is called Bas Osher even though Osher had sons.
*(could be where adoptive father was in kesubah or Get, kosher b'dieved)