Conditions of Udhiyah
Question

I intend to offer a sacrifice on behalf of myself and my children. Are there any specific characteristics that the animal should have, or is it correct to sacrifice any sheep?
Praise be to Allah.There are six conditions for the udhiyah : 
1. It should be one of the an'am class of animals, which are: camels, cattle, sheep and goats, because Allah says (interpretation of the meaning): 
“And for every nation We have appointed religious ceremonies, that they may mention the Name of Allah over the beast of cattle that He has given them for food.” [al-Hajj 22:34]
Bahimat al-an’am (translated here as “beast of cattle”) includes camels, cattle and sheep. This is what is well known among the Arabs, and this was the view of al-Hasan, Qatadah and others. 
2. It should have reached the age stipulated in Shari’ah, which is six months  for a sheep and the age at which the animal is considered to be an adult for any other animal, because the Prophet (peace and blessings of Allah be upon him) said: “Do not sacrifice anything but an adult animal, unless it is difficult for you, in which case you may slaughter a six-month old lamb (jadh’ah).” Narrated by Muslim. 
A mature animal means one that is considered to be an adult.  
In the case of camels, it means one that is five years old. 
For cattle, it means one that is two years old. 
For sheep it means one that is a year old. 
The jadh’ah is that which is half a year old. So it is not correct to sacrifice a camel, cow or goat that has not yet reached maturity, or a sheep that is less than six months old. 
3. It should be free of any faults that would render it unsuitable for sacrifice, of which there are four: 

An obvious defect in one eye, such as when the eye is sunken in its socket, or when it sticks out like a button, or is white and obviously defective. 
Obvious sickness, whose symptoms are clearly apparent in the animal, such as fever that prevents it from grazing and causes loss of appetite; mange that obviously affects its flesh or its health; deep wounds that affect its health, and so on. 
Obvious lameness, which prevents the animal from walking normally. 
Emaciation that leaves no marrow in the bones, when the Prophet (peace and blessings of Allah be upon him) was asked about what should be avoided in udhiyah, he gestured with his hand and said: “Four: a lame animal which is obviously lame, a one-eyed animal whose defect is obvious, a sick animal whose sickness is obvious, and an emaciated animal that no one would choose.” Narrated by Malik in al-Muwatta from the hadih of al-Bara ibn ‘Azib. According to a hadith narrated from him in al-Sunan, he said: “The Messenger of Allah (peace and blessings of Allah be upon him) stood up among us and said: ‘There are four which are not permissible for sacrifice,’” and he mentioned something similar. Classed as sahih by al-Albani in Irwa al-Ghalil, 1148. 

These four faults render an animal unsuitable for sacrifice, and they include similar faults or more severe faults. So the following animals are also unsuitable for sacrifice: 

One that is blind in both eyes.
One that has eaten more than it can stand, until the danger has passed.
One that has encountered difficulty in giving birth, until all danger has passed.
One that has suffered something that could kill it, such as strangulation or a fall from a high place, until the danger has passed.
One that is unable to walk because of a defect.
One that has had one of its forelegs or hind legs cut off.

If these are added to the four defects mentioned in the text, the number of those that cannot be offered as sacrifices reaches ten – these six and the four mentioned above. 
4. The animal should belong to the person who is offering the sacrifice, or he should have permission for that either on the grounds of shari’ah or from the owner. The sacrifice is not valid if the animal slaughtered does not belong to the person who is sacrificing it, such as one that has been taken by force, stolen, or taken on the basis of a false claim, etc, because it is not permissible to draw closer to Allah by means of sin. A sacrifice offered by the guardian of an orphan from the orphan’s property is valid if that is customary and if he feels sad about not offering a sacrifice. 
A sacrifice offered by a guardian from the property of the person under his care is valid, if done with permission. 
5. No one else should have any rights to the sacrificial animal; the sacrifice of an animal that is held in pledge is not valid. 
6. It should be slaughtered at the time specified in Shari’ah , which is from after the ‘Eid prayer on the Day of Sacrifice until sunset on the last of the days of al-Tashriq, which is the 13th of Dhu’l-Hijjah. So the days when the sacrifice may be offered are four: the day of ‘Eid after the prayer, and the three days after that. Whoever slaughters it before the ‘Eid prayer is over, or after sun sets on the 13th of Dhu’l-Hijjah, his sacrifice is not valid, because of the hadith narrated by al-Bukhari from al-Bara ibn ‘Azib (may Allah be pleased with him), according to which the Prophet (peace and blessings of Allah be upon him) said: “Whoever slaughters (his sacrifice) before the prayer, it is meat that he has brought to his family, but that is not the sacrifice.” And he narrated that Jundub ibn Sufyan al-Bajali (may Allah be pleased with him) said: “I heard the Messenger of Allah (peace and blessings of Allah be upon him) saying, ‘Whoever slaughters the sacrifice before he prays, let him replace it with another.’” And it was narrated that Nubayshah al-Hadhali (may Allah be pleased with him) said: “The Messenger of Allah (peace and blessings of Allah be upon him) said: ‘The days of al-Tashriq are the days of eating, drinking and remembering Allah.’” Narrated by Muslim. 
But if he has an excuse for delaying it beyond the days of Tashriq, such as if the animal ran away, without there being any negligence on his part, and he could not find it until after the time was over, or he appointed someone else to slaughter it and that person forgot until the time was over, then there is nothing wrong with slaughtering it after the appointed time. This is by analogy with the one who sleeps and misses a prayer, or forgets it – he should pray it as soon as he wakes up or remembers it. 
It is permissible to slaughter the udhiyah at any time, night or day, but it is better to slaughter it during the day, and it is better to slaughter on the day of ‘Eid after the two khutbahs. Each day is better than the day that follows it, because that means that one is hastening to do good.
And Allah knows best.