What are the most prominent and important works you recommend to help me verify authentic narrations and distinguish them from others?

The science of Hadith, and distinguishing its authentic from its weak narrations, is a noble discipline and a part of the sciences of Islamic law. It requires a gradual study under a specialized shaykh, beginning with concise texts and then moving to more extensive ones. Judging Hadith as authentic or weak is permissible only for deeply rooted imams of Hadith, because a Hadith that is weak through one chain of narration may have another authentic chain, and its weakness should not be declared until an imam from among the Hadith imams has ruled on it.

Among the concise and beneficial books in this science are: "Nukhbat al-Fikr" and its commentary "Nuzhat al-Nazar" by Al-Hafiz Ibn Hajar al-Asqalani. "Al-Mūqiẓah" by Al-Hafiz Al-Dhahabi. "Ikhtiṣār ʿUlūm al-Ḥadīth" by Al-Hafiz Ibn Kathir.

The student then proceeds to more extensive books, such as "Alfiyyat al-Hafiz al-Iraqi" and "Alfiyyat al-Suyuti" and their commentaries.