I asked or someone asked the Prophet ﷺ about perpetual fasting. He replied: You have a duty to your family. Fast during Ramadan and the following month, and every Wednesday and Thursday. You will then have observed a perpetual fast.  

سَأَلْتُ أَوْ سُئِلَ النَّبِيُّ ﷺ عَنْ صِيَامِ الدَّهْرِ فَقَالَ إِنَّ لأَهْلِكَ عَلَيْكَ حَقًّا صُمْ رَمَضَانَ وَالَّذِي يَلِيهِ وَكُلَّ أَرْبِعَاءَ وَخَمِيسٍ فَإِذَا أَنْتَ قَدْ صُمْتَ الدَّهْرَ  

"I asked - or; the Prophet was asked - about fasting daily. So he said: 'Your family has a right over you.' Then he said: 'Fast Ramadan and that which is after it, and every Wednesday and Thursday. If you do that, then you will have fasted daily, as well as broken (the fast).'"  

سَأَلْتُ أَوْ سُئِلَ رَسُولُ اللَّهِ ﷺ عَنْ صِيَامِ الدَّهْرِ فَقَالَ إِنَّ لأَهْلِكَ عَلَيْكَ حَقًّا صُمْ رَمَضَانَ وَالَّذِي يَلِيهِ وَكُلَّ أَرْبِعَاءٍ وَخَمِيسٍ فَإِذًا أَنْتَ قَدْ صُمْتَ الدَّهْرَ وَأَفْطَرْتَ وَفِي الْبَابِ عَنْ عَائِشَةَ  

[Machine] He informed him that the Prophet ﷺ said, "Fast Ramadan and the day after it, and every Wednesday and Thursday, then you have fasted for the entire lifetime." Ibrahim Muslim ibn Ubaidullah said.  

أَخْبَرَهُ أَنَّ النَّبِيَّ ﷺ قَالَ «صُمْ رَمَضَانَ وَالَّذِي يَلِيهِ وَكُلَّ يَوْمِ أَرْبِعَاءَ وَخَمِيسٍ فَإِذًا أَنْتَ قَدْ صُمْتَ الدَّهْرَ» وَقَالَ إِبْرَاهِيمُ مُسْلِمُ بْنُ عُبَيْدِ اللهِ  

"صُمْ رَمَضَانَ وَالَّذِى يَلِيهِ، وَكُلَّ أَرْبَعَاءَ وَخَميسٍ، فَإِذَا أَنْتَ صُمْتَ الدَّهْرَ كلَّهُ وَأَفْطَرْتَ".  

"إِنَّ لأهْلكَ عليكَ حَقًا، صُمْ رمَضانَ والَّذى يليه، وكُلَّ أرْبعَاءَ وخَمِيسٍ، فَإِذا أنْتَ قَدْ صُمْتَ الدَّهْرَ وأَفْطَرْتَ".