Hadith Thaqalayn is one of the traditions reported by about thirty companions of the Holy Prophet (S) and as many as two hundred Sunni scholars have transmitted the same tradition in nearly five hundred books.[1] The documentations of this tradition can be found in the following index, "Sahih Bukhari and Hadith Thaqalayn", question 6921. As for Shia sources, we can give you an example of Shia books such as al-Kafi. It has been reported in this book that the Holy Prophet, peace be upon him and his family, said:

«إِنِّي تَارِكٌ فِيكُمْ أَمْرَيْنِ إِنْ أَخَذْتُمْ بِهِمَا لَنْ تَضِلُّوا كِتَابَ اللَّهِ عَزَّ وَ جَلَّ وَ أَهْلَ بَيْتِي عِتْرَتِی»[2]

“O people! I am leaving behind two things, which if you hold fast to, you will never go astray: the Book of Allah and, the members of my Household, my progeny."
The text of the report transmitted by Ahl-e Sunnah in Sahih Muslim[3], Sahih Timidhi[4] and Musnad of Ahmad bin Hanbal[5] is as such:  "The Book of Allah and my progeny ('itrah)" This is the famous version of the tradition found in their books.
However, there is another text which is not found in Sunnis' authentic books known as Sehāh but Hākim Neishaburi has narrated it in his al-Mustadrak.  In this book, he has collected the traditions and reports which Bukhari and Muslims have left out in their books. Hākim Neishaburi says:

«....عن أبی صالح عن أبی هريرة قال: قال رسول الله (ص): إنی قد تركت فيكم شيئين لن تضلوا بعدهما: كتاب الله و سنتی و لن يتفرقا حتى يردا علی الحوض»

"… From Abi Salih from Abi Hurairah: "The Messenger of Allah (S) said: "I am leaving behind two things, which if you hold fast to, you will never go astray: the Book of Allah and my Sunnah, they shall never separate until they meet me at the Pond."[6]
As it is clear, this tradition has been reported by Abu Hurairah.[7]  The text of this tradition is very similar to the one reported by Sahih Muslim and Musnad of Ahmad. The difference is in "my Sunnah" which has been reported in the two books and other Sunni books as "my progeny".
Superiority of "my progeny, the members of my Household" to "my Sunnah"
A few reasons have been offered to show the superiority of the text, "my progeny, the members of my Household" to "my Sunnah":
1. The narration "my progeny, the members of my Household" has been reported in Sunnis' main books such as Sahih Muslim, Sahih Tirmidhi and Musnad of Ahmad but the narration "my Sunnah", as we mentioned earlier is not mentioned  in any books other than Hākim-e Neishaburi's al-Mustadrak.
2. Hākim-e Neishaburi's narration has been reported only by Abu Hurairah who is never considered to be a reliable narrator according to Shia.  There is yet another version of the tradition with "my companions" instead of "my progeny". This version of the tradition has been reported by people like Abu Sa'eid al-Khidri[8], Zaid bin Arqam[9] and Zaid bin Thabit[10]. This version of the tradition has been reported by more narrators and seems to be better and stronger than the one reported in Hākim-e Neishaburi's al-Mustadrak.
3. The narration which includes "my progeny, the members of my Household" is accepted by both Shia and Sunni sects. That is to say, this text is more acceptable to Muslims across the world than any other versions of the same tradition.
Resolving conflict between the two narrations
1. Based on the foregoing details and considering the great similarity between these two narrations, it can be concluded that there is only one narrative text which is the famous text "my progeny" while the word "sunnati" (my tradition) has been mistakenly or intentionally put in place of "my progeny".  This interpolation reaffirms the fact that Abu Hurairah – as the only narrator of this tradition – and his co-thinkers distanced themselves from the Ahlul-Bayt and progeny of the Prophet (S) after his demise in the event concerning the successorship of the Messenger of Allah (S). In the effort to resolve the conflict, Abu Hurairah's tradition is discredited and rendered invalid.
2. Another probability – though weaker – is that the Prophet (S) may have said both of the traditions i.e. the famous tradition which says, "I am leaving behind two things: "the Book of Allah and my progeny" and he might have said at another place where Abu Hurairah had heard or only he has reported from the Prophet (S) that he said, "the Book of Allah and my Sunnah". In this supposition, there is no dichotomy between the two narrations because the Sunnah of the Prophet (S) is in no way in conflict with the Prophet's household. The household (Ahlul-Bayt) of the Prophet (S) are the ones who best knew the traditions of the Prophet (S) and acted upon them.[11] Hence, the two traditions can be reconciled with each other in the sense that both "my progeny" and "my Sunnah" are acceptable as they confirm each other.
Conclusion:
The tradition with "my progeny, the member of my household" ('itrati ahl- baiti) is not only acceptable to Shia but it is also more famous among Ahl-e Sunnah. The references were provided and it is, therefore, necessary for every fair writer to take these details into consideration in their discussions concerning this topic.

---