Imam Sadiq (PBUH) and Imam Baqir (PBUH) seem to be the most narrated Hadith Imams whose Hadithes are available*
As you might know, several papers of Ahadith were narrated by Imam Hadi (PBUH) that got burnt not a long time later.
Or many Ahadith of Imam Ali (PBUH) had been censored by the government of that time.
According to the chief of the “Hawza-Elmia-Qom Mahdaviat expert center”, it is declared that:
Imam Sadiq (الامام جعفرالصادق علیه السلام) has the most traditions (hadiths) (which have been quoted from him...) as the sixth Imam of Shiite.
In other word, the most hadiths have narrated from him in compare with other Shia Imams. In addition to Imam Jafar-Al-...