This excerpt is taken from Sheikh Zubair Ali Zai Rahimahullah's book "Qurbani ke Ahkam o Masail" (Rules and Issues of Sacrifice).
Sacrifice of Donkey, Mule, and Hinny
A young researcher from Sheikhupura, an advocate of self-made understanding, writes: "Sacrificing animals other than two-toothed animals, such as four-toothed, six-toothed, etc., is not proven from the Sunnah; therefore, four-toothed and six-toothed animals should not be sacrificed."
Reference: (Is the sacrifice of a castrated animal Sunnah? p. 58)
To refute this young researcher and advocate of self-made understanding, consider the following arguments:
1: The Rightly Guided Caliph, Sayyiduna Ali ibn Abi Talib (may Allah be pleased with him), says:
ثنيا فصاعدا واستسمن
"The sacrificial animal should be two-toothed or older, and it should be well-fed and fattened."
Reference: (Al-Sunan al-Kubra by Al-Bayhaqi: 9/373, with authentic chain)
2: Sayyiduna Abdullah ibn Umar (may Allah be pleased with both) says:
فى الضحايا والبدن الثني فما فوقها
"The sacrificial animal should be two-toothed or older."
Reference: (Muwatta Imam Malik: 870, with authentic chain)
From these narrations, it is understood that the condition of ”مسنه“ (two-toothed) is a minimum age requirement; animals that are four-toothed, six-toothed, or older are unanimously permissible with their other conditions.
3: Imam Abu al-Hasan Ibn al-Qattan al-Fasi (may Allah have mercy on him)
Reference: (died 628 AH)
says:وإجماع أنه يجزئ الثني فما فوقه وأنه لا يكون إلا من الأزواج الثمانية
"And there is consensus that the sacrifice of two-toothed and older animals is permissible, and the sacrifice should be from these eight pairs (mentioned in the Qur'an)."
Reference: (Al-Iqna' fi Masa'il al-Ijma': 2/855, paragraph: 1434; Maratib al-Ijma' by Ibn Hazm p. 153)
4: Imam Ibn Abd al-Barr (may Allah have mercy on him) says:
وأجمعوا أن الثني فما فوقه يجزئ منها كلها
"And there is consensus among scholars that the sacrifice of all animals two-toothed and older is permissible."
Reference: (Al-Istidhkar: 4/250)
5: Ibn Battal Abu al-Hasan Ali ibn Khalaf (may Allah have mercy on him)
Reference: (died 449 AH)
says:لا يجوز من سائر الأزواج الثمانية من الأنعام إلا الثني فما فوقه فثني البقر إذا كمل له سنتان ودخل فى الثالثة وثني الإبل إذا كمل له خمس سنين ودخل فى السادسة
"(Except in cases of necessity for the castrated sheep) the sacrifice of any cloven-hoofed animal from the eight pairs is not permissible. The sacrificial animal should be two-toothed or older. Among bulls, two-toothed means the animal has completed two full years and is in the third year; among camels, two-toothed means the animal has completed five full years and is in the sixth year."
Reference: (Sharh Sahih al-Bukhari by Ibn Battal: 6/15)