Has anybody ever compiled a book of Shia authentic Hadiths?

Yes, there are compilations of Shia authentic hadiths. One of the most well-known collections is "Al-Kafi," which is considered a primary source of hadith in Shia Islam. It was compiled by Abu Ja'far Muhammad ibn Ya'qub al-Kulayni al-Razi and includes various narrations covering different aspects of Islamic belief and practice.

Al-Kafi is divided into three main sections: Usul al-Kafi, which deals with theological issues; Furu' al-Kafi, which focuses on practical jurisprudence; and Rawdat al-Kafi, which contains miscellaneous reports. The importance of Al-Kafi is emphasized in Shia tradition, as it is regarded as a reliable source for understanding the teachings of the Prophet Muhammad ﷺ and the Imams.

Furthermore, it is noted that No one among the people has claimed that he gathered the entire Quran as it was revealed except a liar, and the one who gathered it and preserved it as Allah revealed it is only Ali ibn Abi Talib (peace be upon him) and the Imams after him (peace be upon them). Al-Kafi 4:180Shia This illustrates the significance attributed to the teachings and narrations of the Imams in Shia Islam, further supporting the importance of collections like Al-Kafi.