It is not valid to sacrifice a fish, horse, deer or chicken, because one of the conditions of sacrifice is that it must be one of the an’aam animals, which are camels, cattle and sheep of all kinds, because Allaah says (interpretation of the meaning): 

“And for every nation We have appointed religious ceremonies, that they may mention the Name of Allaah over the beast of cattle [an’aam] that He has given them for food”

[al-Hajj 22:34]

It is not reported that the Prophet (peace and blessings of Allaah be upon him) or any of his companions sacrificed any other kind of animal. 

See: Fath al-Qadeer (9/97). 

Al-Nawawi said in al-Majmoo’ (8/364-366): 

The conditions of a sacrifice being valid include that it should be one of the an’aam animals, which are camels, cattle and sheep. All kinds of camels, cattle and sheep, including goats, are acceptable. Other kinds of animals, such as wild cattle, donkeys etc are not acceptable, and there is no difference of scholarly opinion on this point, whether male or female of all kinds, there is no difference of opinion on any of that in our view. 

A cross between a deer and sheep is not acceptable, because it is not an an’aam animal. End quote. 

Ibn Qudaamah (may Allaah have mercy on him) said something similar in al-Mughni (368). 

Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allaah have mercy on him) said in his essay Ahkaam al-Udhiyah wa’l-Zakaah (rulings on sacrifice and zakaah): 

The type (of animal) that may be sacrificed is an’aam animals only, because Allaah says (interpretation of the meaning): 

“And for every nation We have appointed religious ceremonies, that they may mention the Name of Allaah over the beast of cattle [an’aam] that He has given them for food”

[al-Hajj 22:34]

The an’aam animals are camels, cattle, sheep and goats. This was stated by Ibn Katheer who said: This was the view of al-Hasan, Qataadah and others. Ibn Jareer said: This is how it is among the Arabs. End quote. 

And the Prophet (peace and blessings of Allaah be upon him) said: “Do not sacrifice anything but a musinnah; if one is not available then sacrifice a jadh’ah sheep (one that is over a year old).” Narrated by Muslim (1963). A musinnah is a camel, cow or sheep that is two years old or older. This was the view of the scholars (may Allaah have mercy on them). 

The sacrifice is an act of worship, and it should not be done except in the manner narrated from the Messenger of Allaah (peace and blessings of Allaah be upon him), and it is not narrated that he (peace and blessings of Allaah be upon him) sacrificed anything but a camel, cow or sheep. End quote.