I have read in one of your articles that two sons of Hazrat Ali's (rta) were called Usman and Abu Bakr. They were killed in Karbala. Kindly clear this issue giving the reference of some Shi'i books.
This is from among the known facts among the Shia scholars. For instance the very famous Shia Alim, Sheikh al-Mufid writes in Al-Irshad, the section on Tarikh Amir Al-Mumenin, Bab 4 under
ذکر اولاد امير المومنين عليه السلام و عددهم و اسمائهم و مختصر من اخبارهم و عمر و رقيه و العباس و جعفر و عثمان و عبدالله الشهداء مع اخيهم الحسين عليه السلام بطف کربلا ... و محمد الاصغر المکنی بابی بکر و عبيد الله الشهيدان مع اخيهما الحسين عليه السلام بالطف
"and Umar and Ruqayya ... and Abbas and Jafar and Uthman and Abdullah, who (i.e. these four sons) became martyred with their brother Hussain in Karbala ... and Muhammad al-Asghar whose title was Abubakr and Ubayd Allah who became martyrs with their brother Hussain in Karabala ..."
You can find the same details in Muntahi al-Aamal of Sheikh Abbas al-Qumi, Bab 3, Fasl 6.
As a quick reference, look at the following website that is one of the well known Shia sources in Internet where the martyrs of Karbala are listed. Number 7 is Uthman, number 8 is the same Muahammad ibn Ali as above although it does not add that his title was Abubakr, also look at number 9 in the website, Abubkar ibn Hassan ibn Ali, the son of Hassan (ra)