What to Say in the First Tashahhud
Question

I would like you to clarify how to say the Tashahhud in the prayer that contains three and four Rak`ahs. I mean do I have to say the whole Tashahhud in the second Rak`ah? 
Please provide the answer with the evidence from the Quran and Sunnah.
Praise be to Allah.Is the first Tashahhud obligatory?
The first Tashahhud in a three- or four-Rak`ah prayer is obligatory according to the more correct of the two scholarly views. 
There are various versions of the Tashahhud , some of which may be seen in the answer to question no. 98031 . 
Is it obligatory to send blessings on the Prophet after the first Tashahhud?
The scholars differed as to whether it is prescribed to send blessings on the Prophet (peace and blessings of Allah be upon him) after reciting the first Tashahhud. There are two views: 

That blessings should be sent on the Prophet (peace and blessings of Allah be upon him). This is the view of Ash-Shafi`i (may Allah have mercy on him) and he said that one who does not do it should do the prostration of forgetfulness (Sujud As-sahw). The view that it is prescribed was also favoured by Ibn Hazm (may Allah have mercy on him) in Al-Muhalla (2/302). 

Ash-Shafi`i (may Allah have mercy on him) said in Al-Umm (1/228): 
“Tashahhud and blessings on the Prophet (peace and blessings of Allah be upon him) in the first Tashahhud of every prayer except Fajr are two Tashahhuds, first and second. If a person omits the first Tashahhud and sending blessings on the Prophet (peace and blessings of Allah be upon him) in the first Tashahhud by mistake, he does not have to repeat (the prayer) but he has to do the prostration of forgetfulness for forgetting it.”
This view was also favoured by Shaykh `Abd Al-`Aziz ibn Baz and Al-Albani (may Allah have mercy on them). (See: Majmu` Fatawa Ibn Baz, 11/201 and Kitab As-Salah by Al-Albani, p. 145) 

That he should only recite the Tashahhud as far as the Shahadatayn, and not add the blessings on the Prophet (peace and blessings of Allah be upon him). This is the view of the majority of jurists, and was favoured by Shaykh Ibn `Uthaymin (may Allah have mercy on him). 

It says in Al-Mawu`ah Al-Fiqhiyyah (12/39): 
“The majority of jurists are of the view that the worshipper should not add blessings on the Prophet (peace and blessings of Allah be upon him) to the Tashahhud in the first Tashahhud. This is the view of An-Nakha`i, Ath-Thawri and Ishaq (may Allah have mercy on them). 
The Shafi`is are of the view that it is recommended to recite the blessings on the Prophet (peace and blessings of Allah be upon him), and this is the view of Ash-Sha’bi (may Allah have mercy on him). 
But when a person sits at the end of his prayer, there is no difference of opinion among the jurists that it is prescribed to send blessings on the Prophet (peace and blessings of Allah be upon him) after the Tashahhud.”
Shaykh Ibn `Uthaymin (may Allah have mercy on him) said in Ash-Sharh Al-Mumti` (3/225): 
“It is not recommended to send blessings on the Prophet (peace and blessings of Allah be upon him) in the first Tashahhud; this is what may be understood from the Sunnah, because the Prophet (peace and blessings of Allah be upon him) taught Ibn Mas`ud and Ibn `Abbas (may Allah be pleased with them) this Tashahhud only, and Ibn Mas`ud (may Allah be pleased with him) said: We used to say before the Tashahhud was enjoined on us, and he mentioned the first Tashahhud only, and did not mention blessings on the Prophet (peace and blessings of Allah be upon him) in the first Tashahhud . If it was Sunnah then the Messenger (peace and blessings of Allah be upon him) would have taught it to them in the Tashahhud . 
As for their saying “O Messenger of Allah, we know how to send Salam upon you, but how should we send blessings upon you when we send blessings upon you in our prayer?” this was a question about how to do it, and it does not mention when to do it. There is a difference between specifying when and specifying how. Hence Ibn Al-Qayyim (may Allah have mercy on him) said in Zad Al-Ma`ad: It was the way of the Prophet (peace and blessings of Allah be upon him) to shorten this Tashahhud. Then he mentioned the Hadith which says “it was as if he was sitting on a Radaf” i.e., a heated stone, because it was so quick. Even though there is some weakness in the Isnad (chain of narration) of this Hadith, this is what may be understood from the Sunnah, i.e., one should not do any more than that. In Sahih Ibn Khuzaymah it says that the Messenger (peace and blessings of Allah be upon him) used to recite the Tashahhud in this sitting but he did not say Du`a. Despite that, if someone sends blessings on the Prophet (peace and blessings of Allah be upon him) in this place, we would not denounce him, but if he asked us which is better, we would say that limiting it to the Tashahhud only is better, but if he sends blessings on the Prophet (peace and blessings of Allah be upon him), he should not be told not to do that, because it is additional goodness and there is a possibility that it is correct, even though the view that sending blessings on the Prophet at that point in the prayer is weak.”
And Allah knows best.