When refuge is sought in Allah from Satan
Surah al-Mu'minun: verses (97 to 98).
Also, from all the hadiths that teach seeking refuge on various occasions to be protected from Satan's whispers, a general ruling follows: one remedy for every kind of satanic whisper is seeking refuge in Allah.
When the adhan is called1
When you recite the Sunnah remembrances and the Quran2
The hadiths of Sahih al-Bukhari (608), Sahih Muslim (389) and others establish that Satan flees from the adhan called for the prayer. But does Satan also flee from an adhan that is not for the prayer? That needs proof; rather, calling the adhan merely to drive Satan away, apart from the prayer, is itself not established.
Some narrations mention calling the adhan to drive Satan away, but these narrations are weak; see: [Musnad Ahmad, Maymaniyyah edition (3/305), Musannaf Abd ar-Razzaq, ed. al-A'zami (5/160), and al-Albani graded it Da'eef in ad-Da'ifah no. (1140)].
At-Tabarani and others have some more narrations on this, which are mawdu' and fabricated. In short, no hadith at all is established about calling the adhan specifically to drive Satan away.
There is a sahih hadith: Do not make your houses graveyards; Satan flees from a house in which Surah al-Baqarah is recited, (Sahih Muslim, no. 780). Satan also flees when the following are kept up:
The morning and evening remembrances, the remembrances for sleeping and waking, the supplications for entering and leaving the house, the supplications for entering and leaving the mosque, and all the other Sunnah remembrances, for example reciting Ayat al-Kursi and the last two verses of Surah al-Baqarah at bedtime. Likewise, on the day someone says “لَآ اِلٰهَ اِلَّا اللّٰهُ وَحْدَهٗ لَا شَرِيْكَ لَهٗ ، لَهُ الْمُلْكُ وَلَهُ الْحَمْدُ وَهُوَ عَلٰى كُلِّ شَيْءٍ قَدِيْرٌ” a hundred times, he will be protected from Satan that day; see page (105) of this book. Likewise, the adhans (for the prayers) also drive Satan away.