In the Little House on the Prairie book series by Laura Ingalls Wilder, the Ingalls family did not adopt any children, nor did they adopt any in real-life. Laura and her siblings were all biological children of Charles and Caroline Ingalls.
The confusion about whether the Ingalls actually adopted any children is due to the creative license that the television show took with the Ingalls family. The real Ingalls family never adopted Albert, nor is there anyone in the Ingalls real life that the character of Albert was based upon.