The most excellent fast after Ramadan is God's month. al-Muharram, and the most excellent prayer after what is prescribed is prayer during the night.  

قَالَ رَسُولُ اللَّهِ ﷺ أَفْضَلُ الصِّيَامِ بَعْدَ رَمَضَانَ شَهْرُ اللَّهِ الْمُحَرَّمُ وَأَفْضَلُ الصَّلاَةِ بَعْدَ الْفَرِيضَةِ صَلاَةُ اللَّيْلِ  

he attributed this to the Prophet ﷺ: He was asked which prayer is best after the obligatory prayers and which fasting is best after the month of Ramadan? He said: (1) The best prayer after the obligatory prayers is the one offered in the middle of the night, and (2) the best fast after the month of Ramadan is the fast in the Month of Allah: al-Muharram.  

سُئِلَ أَىُّ الصَّلاَةِ أَفْضَلُ بَعْدَ الْمَكْتُوبَةِ وَأَىُّ الصِّيَامِ أَفْضَلُ بَعْدَ شَهْرِ رَمَضَانَ فَقَالَ أَفْضَلُ الصَّلاَةِ بَعْدَ الصَّلاَةِ الْمَكْتُوبَةِ الصَّلاَةُ فِي جَوْفِ اللَّيْلِ وَأَفْضَلُ الصِّيَامِ بَعْدَ شَهْرِ رَمَضَانَ صِيَامُ شَهْرِ اللَّهِ الْمُحَرَّمِ  

A hadith like this has been reported from the Messenger of Allah ﷺ by 'Abd al-Malik with the same chain of transmitters in connection with fast.  

عَنِ النَّبِيِّ ﷺ بِمِثْلِهِ