I used to read that Yazdegerd III, the King of Kings when Iran was conquered by the Arabs, was 15 years old when he came to the throne in 632, and thus born about 617. Obviously Yazdegerd the Third was born before his father Shahriyar, son of Khosrow II and Shirin, was killed, or at most 9 months after Shahriyar was killed, if he was posthumous.
Shahriyar was killed by his half brother, the new King of Kings Sheroe or Kavad II, in 628, possibly on 25 February, the day of Kavad's coup against KHosrow II. Yazdegerd was crowned on 16 June 632, and so could have been only 3 or 4 years old then if he was posthumous. So Yazdegerd III was probably born sometime during the period of about 616 to 629.
Some time ago I read that Yazdegerd was probably much younger than 15 when he became King of Kings, and I think there was a statement that the Iranian coins did not show Yazdegerd with a beard for many years after 632, so he was probably much younger than than 15 when he became monarch.
Last night I found that the Wikipedia article on Yazdegerd the Third says he was born in 624. And else where it says that:
Most scholars agree that Yazdegerd was eight years old at his coronation.4 [Wikipedia:Yazdegerd_III#Background]
3Kia, Mehrdad (2016). The Persian Empire: A Historical Encyclopedia [2 volumes]: A Historical Encyclopedia. ABC-CLIO. ISBN 978-1610693912. p. 284.
Yazdegerd III. The last monarch of the Persian Sasanian dynasty (r. 224-651 CE) who ascended the throne at the age of eight in...
5 Shahbazi, A. Shapur (2005). "Sasanian dynasty". Encyclopaedia Iranica, Online Edition. Retrieved 4 January 2014.
When Farroḵ Hormozd was assassinated in a palace plot, his son Rostam brought his forces to Ctesiphon, murdered the queen, and enthroned Yazdegerd (III), a grandson of Ḵosrow then merely eight years old (Ṭabari, I, p. 1067).
 Pourshariati, Parvaneh (2008). Decline and Fall of the Sasanian Empire: The Sasanian-Parthian Confederacy and the Arab Conquest of Iran. London and New York: I.B. Tauris. ISBN 978-1-84511-645-3. p. 257
And apparently Pourshariati says that the historian Tabari says that Yazdegerd III lived for 28 years, making him 8 when he ascended the throne.
And what does Wikipedia say about his son Peroz III?
Prince Peroz was born in 636,5 and was thus very young at the time of the reign of his father king Yazdegerd III and never exercised the imperial power of the Sasanians. After the Arab conquest of Iran, Peroz and much of the imperial family escaped through the Pamir Mountains in what is now Tajikistan and arrived at Tang China, which was more supportive of the Sasanians.
5 Compareti 2009. Compareti, Matteo (2009). "Chinese-Iranian relations xv. The last Sasanians in China". Encyclopaedia Iranica.
In the Jiu Tangshu there is a considerable confusion between the figures of Peroz and Narseh, while in the Xin Tangshu it is clearly stated that after 679 it was Narseh who fought in Ṭoḵārestān against the Arabs, as already argued by some scholars on the basis of the age of Peroz (Drake, pp. 6-7). According to Herzfeld (p. 94), Peroz was born in 636, a date which could be considered well-fitting for the general history of late Sasanians and for the events narrated in the Chinese chronicles.
Drake pp. 6-7 hsould be in:
F. S. Drake, “Mohammedanism in the Tang Dynasty,” Monumenta Serica 8, 1943, pp. 1-40.
And Herzfeld, p. 94 should be in:
E. Herzfeld, “Khusrau Parwēz und der Tāq i Vastān,” AMI 9, 1938, pp. 91-158.
So there seem to be scholarly discussions of the birthdate of Peroz III.
So Yazdegerd III was supposedly born in 624 and his son Peroz III was supposedly born in 636.
But so far the only source I noted for Yazdegerd's birth is Tabari's statement that he lived for 28 years. I don't know when in 651 Yazdegerd was killed.
If Yazdegerd was killed sometime between the beginning and end of 651 and was between 28 and 29 years old at that time, he would have been born between 622 and 624, and so would have been about 12 to 14 years old when Peroz was born in 636.
If there is an independent source claiming that Yazdegerd was eight years old when he became King of Kings on 6 June 632, that would mean he was born between 7 June 623 and 6 June 624, and was about 12 or 13 when Peroz was born.
So obviously there is a possibility that Yazdegerd III was one of the youngest royal fathers in history, perhpas being only 12 years older than Peroz III. And 12 years is the youngest proven age for any royal father I know of, though there are possible younger examples.
I note that there is a possible motive for Tabari or his sources to want to make Yazdegerd III born as late as possible.
The various descendants of Ali, and their Shiite followers sought to become Caliphs of Islam, and the Caliphs in power sought to defeat their revolts and discredit their ideology. Thus the subject of Alid genealogy was quite controversial during the middle ages.
It is said by Shiites that Yazdegered III's daughter Shahbrbanu was captured and brought to Mecca and married to Huseyn ibn Ali, the Shiite Iman, and that their son was Ali ibn Huseyn Zayn al-Abidin, the next Iman, who has alleged descendants down to the present.
Ali ibn Huseyn Zayn al-Abidin survived the disaster at Karbala in 680. And I have sometimes read that he was spared because he was a boy at the time.
But if I remember correctly, Tabari claimed that stories that Ali was a boy in 680 were incorrect and he was actually an adult by them. And as I wrote above, an online excerpt from Pourshariati, Parvaneh (2008). Decline and Fall of the Sasanian Empire: The Sasanian-Parthian Confederacy and the Arab Conquest of Iran. London and New York: I.B. Tauris. ISBN 978-1-84511-645-3. p. 257 credits Tabari with the statement that Yazdegerd III was 28 when he was killed in 661.
And that seems to be the source for statements that Yazdegerd II was 8 in 632 and born in 624.
The Wikipedia article on Ali ibn Huseyn Zayn al-Abidin says:
Ali ibn al-Husayn was born in Medina in the Hejaz, now in Saudi Arabia, in the year 38/658–9.[b]
b. Other dates mentioned are 33/653–4, 36/656–7, 37/657–8, 50/670
And note 15 says: pp. 7-10 of Imam Ali ubnal Husain (2009). Al-Saheefah Al-Sajjadiyyah Al-Kaamelah. Translated with an introduction and annotation by Willian C. Chittick with a foreword by S. H. M. Jafri. Qum, The Islamic Republic of Iran: Ansariyan Publications.
Note that if Ali was born in 659 and Yazdegerd was born in 624, a difference of 35 years, that would make an average of about 17.5 years per generation.
So it is possible that Tabari, or his sources, tried to depict Yazdegerd as being born as late as possible, and Ali as being born as early as possible, to discredit claims that Ali's mother was a daughter of Yazdegerd.
I note that with a possible birth year of 624 for Yazdegerd, and the range of alleged birth years of Ali ranging from 653 to 670, the time span could be between 29 and 46 years, and the average generaton between 14.5 and 23 years.
My answer dated March 16, 2021 to this question:
Discusses the cases of a number of allgedly very young royal fathers, some of them as young as 12.
Discusses the possible genealogical links between the Sassanian dynasty of Kings of Kings, the Khagans of the Turks, Roman Emperors of two different dynasties, the House of David, and members of the Arab Quraysh tribe of Mecca.
The possible connections are really interesting, and the uncertainty frustrating.
Also see post number 6 there.
And here is a link to another question on that topic: