Ibn Khuzaymah

And the explanation of the evidence that the Prophet ﷺ, in the narration of Abu Sa'id (may Allah be pleased with him), commanded that (the one who hears the adhan) should say just as the muezzin says, until he (the muezzin) finishes (the adhan), and you ﷺ would also say just as the muezzin says, until he becomes silent, except for "Hayya 'ala as-Salah" and "Hayya 'ala al-Falah" (for their response).

Sayyiduna Isa bin Talhah (may Allah be pleased with him) narrates that we were present in the company of Sayyiduna Muawiyah (may Allah be pleased with him) when the muezzin called the adhan for prayer. He said « اللهُ أَكْبَرُ، للهُ أَكْبَرُ » "Allah is the Greatest, Allah is the Greatest," so Sayyiduna Muawiyah (may Allah be pleased with him) also said « اللهُ أَكْبَرُ، للهُ أَكْبَرُ ». Then he said « أَشْهَدُ أَنْ لَا إِلَهَ إِلَّا اللهُ » "I bear witness that there is no deity worthy of worship except Allah," so Sayyiduna Muawiyah (may Allah be pleased with him) also said « أَشْهَدُ أَنْ لَا إِلَهَ إِلَّا اللهُ ». Then he said « أَشْهَدُ أَنْ مُحَمَّدٌ رَسُولُ ٱللَّٰه » "I bear witness that Muhammad (peace and blessings be upon him) is the Messenger of Allah." Then he said « حَيَّ عَلَى الصَّلَاةِ » "Come to prayer," so Sayyiduna Muawiyah (may Allah be pleased with him) said « لَا حَوْلَ وَلَا قُوَّةَ إِلَّا بِاللَٰهِ » "There is no power to avoid sin nor strength to do good except with Allah's help." Then he said « حَيَّ عَلَى الْفَلَاحِ » "Come to success," so Sayyiduna Muawiyah (may Allah be pleased with him) said « لَا حَوْلَ وَلَا قُوَّةَ إِلَّا بِاللَٰهِ » "There is no power to avoid sin nor strength to do good except with Allah's help." Then he said that I heard your Prophet (peace and blessings be upon him) responding to the adhan in this manner.