What is the ruling on an inadvertent addition to the prayer, such as reciting a surah or the Basmalah after Al-Fatihah in the third and fourth rak'ahs of a fard prayer, or reciting the Ibrahimiya prayer (or part of it) in the middle Tashahhud?

If a congregant (ma'mum) adds the Basmala or a surah in the wrong place, they are not required to perform the prostration of forgetfulness (sujud al-sahw). However, if they are praying alone (munfarid) or leading the prayer (imam), then some scholars hold that it is recommended (mustahabb) to perform the prostration of forgetfulness. If one recites all or part of the Ibrahimiyya prayer in the first tashahhud, there is absolutely no prostration of forgetfulness required.