What is the ruling regarding someone who prayed ʿAsr and his brother doubted that he had performed only one prostration in the second rakʿah, knowing that the doubt occurred during the prayer and that the brother is not certain?

As long as you are certain that you did not miss a prostration, do not pay attention to the statement of the congregant, because the certainty of the Imam takes precedence over the certainty, assumption, and doubt of a single congregant. The Imam does not refer to the words of the congregants unless they are very numerous. As for the congregant who is certain that the Imam added something, he should not follow him. If he follows him, his prayer becomes invalid if he was aware of the addition and the impermissibility of following. However, if he was ignorant, his prayer is not invalidated if he rectifies the situation.