How is the authenticity of a Prophetic Hadith verified, or an narration transmitted from a Companion or a Successor?

The method for ascertaining the authenticity of a Hadith is to research who narrated it. If it was narrated by someone who committed to authenticity, such as Al-Bukhari and Muslim, or Ibn Khuzaymah, Ibn Hibban, and Al-Hakim (provided the memorizers of Hadith did not criticize it), then it is authentic.

Otherwise, search for it in books of Hadith extraction (Takhrij) and see if any of the memorizers of Hadith, such as Ibn Hajar, or later scholars, such as Al-Albani, commented on it. If they ruled it authentic, then it is authentic, as Al-Suyuti indicated.

If you do not find anyone who commented on its authenticity, then apply the criteria for an authentic Hadith: namely, a continuous chain of narration (isnad) by trustworthy and precise narrators, without any irregularity (shudhudh) or damaging defect (illah).

It is important to note that the statement by some Hadith extractors, "Its chain of narration is authentic," does not always necessitate that the chain is continuous or free from defects and irregularities.

For further detail, one can refer to books of Hadith terminology, such as "Muqaddimat Ibn al-Salah" and "Alfiyat al-Iraqi wa al-Suyuti."