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.
أَنَّ فِي حَدِيثِ حَاتِمٍ وَإِنَّ رَسُولَ اللَّهِ ﷺ 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