Adopting a foundling

Q: One of my relatives found a baby, whose age at that time was just a few hours old. She informed me about this; and she is poor, trying to earn her living by hard work. Thus, I decided secretly to do the following: I talked to my wife in this respect and agreed to bring up and adopt the baby, (Part No. 11; Page No. 257) seeking the Satisfaction of Allah. Allah (Exalted be He) will provide us with the means of subsistence for bringing up this baby, who is not to blame for this horrible crime. I feared that the baby may become ill-bred and fall into the trap of sin and perversity. Allah (Exalted be He) knows best that I had a good intention; and did not know at that time from the Qur'an about adoption except the Ayah (Qur'anic verse), in which Allah (Glorified and Exalted be He) speaks about His honorable Messenger (peace be upon him): Muhammad (صلى الله عليه وسلم) is not the father of any of your men, but he is the Messenger of Allâh and the last (end) of the Prophets. As far as I knew at the time, this Ayah is only related to the Prophet (peace be upon him). I registered my name as the father of the baby lest the baby should be looked at in a disgraceful way. I did not register either in the police reports or in any other documents that this baby is my adopted son. After nine years, Satan started to insinuate my wife that this boy is actually my son from another wife. Row triggered between us, and she claimed that she wanted to know the permissibility of having this boy among us, and the legal opinion regarding this matter. It is worth mentioning that she breast-fed him three months after weaning her son. However, the baby was not able to suck at her breast, and she dropped milk into his mouth more than once. Now, after nine years and the problem has become severe, I could not prove that this baby is my adopted son, because (Part No. 11; Page No. 258) he is registered in the official documents as my son. I hope you will reveal to me and to my wife whether what we did is Haram (unlawful), for which we will be accounted, even though I did not know and had a good intention seeking only Allah's Pleasure. I hope you will tell me what to do and the child is now nine years old, and all of the people and his brothers know that he is my son. Please inform us by an official letter so I can live peacefully with my wife. May Allah benefit you.