What is the authenticity of attributing children to the father in cases of adoption, and does this contradict the noble Hadith: "Any woman who introduces someone to a people who is not of them, then she is not from Allah in anything"?

There is no contradiction between the hadith and the attribution of children to you. If your wife has given birth to children from someone other than you and has attributed them to you, she has committed a grave sin. As for the children, they cannot be disclaimed by you except through li’an from your part, even if their mother admits that they are from someone other than you, for the child belongs to the marriage bed. One must submit to the ruling of the Messenger of Allah, peace and blessings be upon him.