Some people give the 8 Rakaat Taraweeh daleel from a Daeef hadith by Hadhrat Jaber Radhi Allahu Anhu. Lets see what the Muhaqqiq of Saheeh Ibne Hibban Shoaib Arnaut says about it. Very clearly states that it is Daeef :

“إسناده ضعيف. عيسى بن جارية ضعيف، قال ابن معين: عنده مناكير، وقال النسائي: منكر الحديث، وجاء عنه: متروك، وقال ابن عدي: أحاديثه غير محفوظة، وقال أبو زرعة: لا بأس به. أبو الرسغ الزهراني: هو سليمان بن داود العتكي، ويعقوب القمي: هو ابن عبد اللهالأشعري.
وأخرجه المروزي في “قيام الليل وكتاب الوتر” كما في “مختصره ” للمقريزي، ص 118 عن إسحاق بن إبراهيم، بهذا الإِسناد.
وأخرجه الطبراني في “الصغير” (525) ، وابن خزيمة (1070) ، من طريق يعقوب القمي، بهذا الإِسناد.
قال الهيثمي في “المجمع” 3/172: فيه عيسى بن جارية وثقه ابن حبان، وضعفه ابن معين. وسيرد برقم(2415) ”


Also check:

1. Imam ibn A’adi r.h states: The hadith that is narrated by Isa Bin Jaariya is “not” preserved. ( Tehzeeb At Tehzeeb : 186 /8 , Tehzeeb Al Kamaal : 533 , 534 /14 , Mizaan Ul Aitedaal : 311/3)

2. Imam Aqeeli r.h has classified Isa Bin Jaariya amoungst Da’eef(weak) narrators. (Tehzeeb At Tehzeeb : 186 /8 , Tehzeeb Al Kamaal : 533 , 534 /14 , Mizaan Ul Aitedaal : 311/3)

In the blessed month of Ramadan people try there best to attend the Taraweeh Salaah and they should also do the same with Tahajjud Salaah during Ramadan since both of them are separate and are not the same. Some people claim that they are the same but that is not the truth and in this post we will see some of the daleel that they are both separate from one another. 

1 –Hadhrat Umar Al Farooq Rdh. Al Mutawaffa 23 Hij.

Hadhrat Ameer ul Momineen Umar bin Khattab Rdh. Al Mutawaffa 23 Hij. says:

The prayer for which you sleep (meaning Tahajjud) is Afzal (better) than the one for which you are doing Qayyam (meaning Taraweeh) 

(Saheeh Bukhari : Hadith No. 2010)

Hadhrat Umar Rdh. is encouraging us to offer Tahajjud as well after Taraweeh, since it is a permanent prayer. This is the reason that the Muhaddiseen have classified Taraweeh and Tahajjud separately and have also stated it very clearly.

a. - Imam Abul Wali Sulaimaan al Baaji al Qurtubi Rh. Al Mutawaffa 474 Hij. 

Says about the saying of Hadhrat Umar Rdh. that the Qiyaam in the later part of the night is superior (Afzal) then the part of night in which Qiyaam was before it. 

(Al Muntaqa Lil Baaji : Volume 1 : Page 208)

Some people say that the dua  اللَّهُمَّ لَكَ صُمْتُ، وَعَلَى رِزْقِكَ أَفْطَرْتُ is not proven from Prophet Muhammad ﷺ and the hadith which has these words is weak (Daeef). 

Below is the Daleel and Analysis on this issue:

1. 

حَدَّثَنَا ابْنُ فُضَيْلٍ، حَدَّثَنَا حُصَيْنٌ، عَنْ أَبِي زُهْرَةَ، قَالَ: كَانَ النَّبِيُّ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ إِذَا صَامَ، ثُمَّ أَفْطَرَ يَقُولُ: «اللَّهُمَّ لَكَ صُمْتُ، وَعَلَى رِزْقِكَ أَفْطَرْتُ»

In the above hadith, it is mentioned by Abu Zohra Rh. that when it s time for Iftaar, they recited: اللَّهُمَّ لَكَ صُمْتُ، وَعَلَى رِزْقِكَ


(Ad- Duaa Liz Zabbai : Hadith No 66)