Who are the Tabi‘in? And who are those who came after the Tabi‘in?
Question

Who are the Tabi‘in? And who are those who came after the Tabi‘in?
Praise be to Allah.Firstly:
The Tabi‘in are those who came after the time of the Prophet (blessings and peace of Allah be upon him) and did not meet the Messenger of Allah (blessings and peace of Allah be upon him); rather they met the Companions of the Prophet (blessings and peace of Allah be upon him) and learned from them.
Those who came after of the Tabi‘in are those who did not meet the Companions of the Messenger of Allah (blessings and peace of Allah be upon him); rather they met the Tabi‘in and learned from them.
The Tabi‘i, in hadith terminology, is the one who met the Companion, but it is not stipulated that he should have spent a long time with him, according to the correct view. Anyone who met the Companions and died as a Muslim is a Tabi‘i, and some of them are better than others.
Al-Hafiz Ibn Hajar (may Allah have mercy on him) said in Nukhbat al-Fikr (4/724): The Tabi‘i is the one who met the Companion. End quote.
Ibn Kathir (may Allah have mercy on him) said:
Al-Khatib al-Baghdadi said: The Tabi‘i is the one who met the Companion. From the words of al-Hakim, it may be understood that the name Tabi‘i may be applied to the one who met the Companion and narrated from him, even if he did not spend time with him. End quote.
Al-‘Iraqi (may Allah have mercy on him) said in his Alfiyah (p. 66):
The Tabi‘i is the one who met the one who accompanied [the Prophet (blessings and peace of Allah be upon him)].
Those who came after the Tabi‘in are those who met the Tabi‘in but did not meet the Companions (may Allah be pleased with them).
The Tabi’in include people such as: Sa‘id ibn al-Musayyib, ‘Urwah ibn az-Zubayr, al-Hasan al-Basri, Muhajid ibn Jabr, Sa‘id ibn Jubayr, ‘Ikrimah the freed slave of Ibn ‘Abbas, and Nafi‘ the freed slave of Ibn ‘Umar.
Those who came after the Tabi‘in include people such as ath-Thawri, Malik, Rabi‘ah, Ibn Hormuz, al-Hasan ibn Salih, ‘Abdullah ibn al-Hasan, Ibn Abi Layla, Ibn Shubrumah and al-Awza‘i.
Secondly:
Al-Bukhari (3651) and Muslim (2533) narrated from Ibn Mas‘ud (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) said: “The best of people are my generation, then those who come after them, then those who come after them. Then there will come people whose testimony will come before their oath, and their oath before their testimony.”
An-Nawawi (may Allah have mercy on him) said:
The correct view is that his generation were the Companions, the second generation were the Tabi‘in, and the third generation were those who came after the Tabi‘in."(Sharh an-Nawawi ‘ala Muslim 16/85).
Al-Hafiz Ibn Hajar (may Allah have mercy on him) said:
The words “then those who come after them” mean the generation who followed them, namely the Tabi‘in, and “then those who come after them” refers to the generation who came after the Tabi‘in."(Fath al-Bari  7/6).
Al-Qari (may Allah have mercy on him) said:
As-Suyuti said: The correct view is that this word – al-qarn (generation) – does not have a defined duration. The Prophet’s generation, namely the Companions, lasted from the time his mission began until the last of the Companions died, approximately one hundred and twenty years. The generation of the Tabi‘in lasted until approximately 170 AH, and the generation of those who came after the Tabi‘in lasted until approximately 220 AH. During this time, innovations appeared and became widespread, the Mu‘tazilah began to preach their misguided notions, philosophers began to spread their misguided ideas, the scholars were put to trial and forced to say that the Qur’an was created, and circumstances changed drastically, and things have only been getting worse until now. This is a confirmation of the words of the Prophet (blessings and peace of Allah be upon him): “Then lying will become widespread.”"(Mirqaat al-Mafatih  9/3878).
And Allah knows best.