This tradition has been narrated by the game authority (Yazid b. Hurmus) through a different chain of transmitters with the following difference in the elucidation of one of the points raised by Najda in his letter to Ibn Abas: The Messenger of Allah (ﷺ) used not to kill the children, so thou shouldst not kill them unless you could know what Khadir had known about the child he killed, or you could distinguish between a child who would grow up to he a believer (and a child who would grow up to be a non-believer), so that you killed the (prospective) non-believer and left the (prospective) believer aside.
Source: sunnah.com
Other translations
Arabic
حَدَّثَنَا أَبُو بَكْرِ بْنُ أَبِي شَيْبَةَ، وَإِسْحَاقُ بْنُ إِبْرَاهِيمَ، كِلاَهُمَا عَنْ حَاتِمِ بْنِ إِسْمَاعِيلَ، عَنْ جَعْفَرِ بْنِ مُحَمَّدٍ، عَنْ أَبِيهِ، عَنْ يَزِيدَ بْنِ هُرْمُزَ، أَنَّ نَجْدَةَ، كَتَبَ إِلَى ابْنِ عَبَّاسٍ يَسْأَلُهُ عَنْ خِلاَلٍ، . بِمِثْلِ حَدِيثِ سُلَيْمَانَ بْنِ بِلاَلٍ غَيْرَ أَنَّ فِي، حَدِيثِ حَاتِمٍ وَإِنَّ رَسُولَ اللَّهِ صلى الله عليه وسلم لَمْ يَكُنْ يَقْتُلُ الصِّبْيَانَ فَلاَ تَقْتُلِ الصِّبْيَانَ إِلاَّ أَنْ تَكُونَ تَعْلَمُ مَا عَلِمَ الْخَضِرُ مِنَ الصَّبِيِّ الَّذِي قَتَلَ . وَزَادَ إِسْحَاقُ فِي حَدِيثِهِ عَنْ حَاتِمٍ وَتُمَيِّزَ الْمُؤْمِنَ فَتَقْتُلَ الْكَافِرَ وَتَدَعَ الْمُؤْمِنَ .
sunnah.com