Are there any authentic Prophetic Hadiths whose rulings have been abrogated by other authentic Hadiths, and what are examples of them?

There are authentic Hadiths abrogated by other authentic ones. Examples include:

1. The Hadith "Water (ghusl) is only from water (semen)" narrated by Abu Sa'id al-Khudri, which implies that ghusl is not obligatory unless there is ejaculation. This was abrogated by the Hadith, "When one sits between its four branches and the circumcised part touches the circumcised part, then ghusl becomes obligatory." There is now a consensus that ghusl is obligatory for intercourse, even if there is no ejaculation.

2. Hadiths permitting temporary marriage (mut'ah), which were abrogated by other authentic and explicit Hadiths, including the Hadith of Salama ibn al-Akwa': "The Messenger of Allah (peace and blessings be upon him) permitted mut'ah during the year of Awtas for three days, then he forbade it." Its prohibition has been definitively established until the Day of Judgment by the consensus of the Ummah, with only a group of innovators dissenting.

There are many authentic Hadiths abrogated by similar ones. As for abrogation in the Quran, it has been detailed in another fatwa.