There is something called shia and sunni hadith. The ahadith that these shia invented to support their belief is shia hadith and you won't find their obvious ones in the muslim ahadith books.
From: syed-mohsin naquvi
Besides, there are no Shia HAdeeth and there is no Sunni Hadeeth. There is just HAdeeth.
For your kind perusal
The most famous collectors of the Sunni Hadith were al-Bukhari (Sahih), Muslim (Muslim), Abu Dawud, at Tirmidhi, an-Nasai and ibn Maja. All these compilers died between 256 to 303 years after the Hijrah (or between 870 to 915 AD). The Shiah collections of hadith are called khabar and were compiled even later, between 320 to 454 after the Hijrah (or between 932 to 1062 AD). The five recognized Shiah compilers were Abu Jafar (Kafi), Saykh Ali (Man la yastihzau-hu al Faqih), Shaykh Abu Jafar (Tahdhib and Istibsar) and Sayyid al-Razi (Nahj al-Balaghah) .