Imam Ibn Kathir رحمہ اللہ writes:
Yazeed ibn Muawiya had twenty childrens, including fifteen boys and five girls and he mentioned the names of the girls and boys and said:
وقد انقرضوا كافة فلم يبق ليزيد عقب، والله سبحانه أعلم
Verily, all these childrens perished and his lineage was completely ended and Allah swt is all knowing.
[al Bidayah wan Nihayah 5/751]
He further writes:
انه لم يمهل بعد وقعة الحرة وقتـل الحسين الايسيرا حتى قصمه الله الذي قصم الجبابرة قبله وبعده انه كان عليما قديرا
"It did not take long after the incident of Harra and the killing of Saydna Hussain until Allah made him taste the same fate, like he destroyed the tyrants before and after him. Indeed, He is All Knowing, All Powerful."
Imam Dhahabi رحمہ اللہ writes regarding Yazeed:
افْتَتَحَ دَوْلَتَهُ بِمَقْتَلِ الشَّهِيْدِ الحُسَيْنِ، وَاخْتَتَمَهَا بِوَاقِعَةِ الحَرَّةِ، فَمَقَتَهُ النَّاسُ، وَلَمْ يُبَارَكْ فِي عُمُرِه
His reign started with martyrdom of Saydna Hussain and ended with the event of Harrah. People hated him and he had no blessings in his age (he lived very short life).
[Seyr Alam an Nubala 4/37]
Allama Mohammad Abdur Rashid Naumani writes:
Yazeed wanted to end the lineage of Saydna Hussain رضیﷲ عنه but Allah had different plans. After some time, the descendants of Saydna Hussain رضیﷲ عنه spread across the four corners of the world, and today, the descendants of Hussain can be found in various regions of the Islamic world. However, the lineage of Yazid was destined to be destroyed from that very era, to the extent that its existence vanished from the surface of the earth. Ibn Kathir, in his book 'Al-Bidayah wa An-Nihayah,' has mentioned the twenty-two offspring of Yazid ibn Muawiya, none of whom were remembered by their name. Among them were fifteen boys and five girls."
[Hadesa Karbala ka Pase Manzar pg. 160]
