This excerpt is taken from Sheikh Farooq Rafi Sahib's book Qurbani, Aqiqa, and Ashra Zil-Hijjah.
There are different opinions among scholars regarding the determination of the age of Juz'ah:
① According to the majority of scholars, a sheep's Juz'ah is one that has completed one year of age.
② A six or seven-month-old lamb of a sheep is called Juz'ah.
③ According to one opinion, an eight-month-old lamb of a sheep, and according to another opinion, a ten-month-old lamb of a sheep is Juz'ah.
Reference: Fath al-Bari 8,7/10. Sharh al-Nawawi 118/13
Preferred Opinion:
① Imam Nawawi, may Allah have mercy on him, states:
والجذع من الضأن، ما له سنة تامة هو الأصح عند أصحابنا، وهو الأشهر عند أهل اللغة وغيرهم
"A complete one-year-old lamb is called Juz'ah, and according to our companions (Shafi'is), this is the preferred opinion, and among the linguists and other scholars (majority), this opinion is more famous."
Reference: Sharh al-Nawawi 118/13
② Hafiz Ibn Hajar, may Allah have mercy on him, writes:
هو وصف لسن معين من بهيمة الأنعام، فمن الضأن ما أكمل السنة وهو قول الجمهور
(Juz'ah) is a description of an animal of a specific age among the cattle (camel, cow, sheep, goat), and the Juz'ah of a sheep (Kheera) is one that has completed a full year. This is the opinion of the majority of scholars. (Then he mentions other opinions about Juz'ah related to the form of illness and declares them less preferred)."
Reference: Fath al-Bari: 10/7
③ Ibn Athir Jazari writes:
ومن الضأن ما تمت له سنة
"The Kheera (Juz'ah) of a sheep is one that has completed a full year."
Reference: Al-Nihayah fi Gharib al-Hadith: 713/1