Is the prostration of forgetfulness prescribed for the regular Sunnah prayers, and is there a specific supplication for it?

Whoever forgets during their prayer—whether obligatory or supererogatory—is prescribed to perform the prostration of forgetfulness (sujud al-sahw); due to the generality of the evidence which does not differentiate between obligatory and supererogatory prayers. In it, one performs two prostrations, and it is sunnah to say the same remembrances and supplications as are said in the prostrations of the prayer itself.