Aqiqah for an illegitimate child
In the name of Allah, the most Beneficent, the most Merciful.
The performance of aqiqah is highly encouraged. It is to be performed by the parents or the guardian of the child.
The Prophet of Allah Sallallahu Alahi Wasalam has said that a child is pledged to its aqiqah which is sacrificed on behalf of the child on the seventh day when it is given a name and the hair is shaved off its head. (Sunan Tirmizi p.278 v.1)
With regards to your question it is still encouraged to do an aqiqah for the child irrespective of whether the parents are married or not as the purpose of aqiqah is to remove the impurities of the child and save it from all types of calamities. (Bashti Zewar p.280)
Aqiqah should be performed on the seventh day of the birth of the child and if not done on the seventh day then whenever it is done, it should be on the next seventh day and so on. (Ibid)
One can do aqiqah even though the child has reached puberty. (Ahsanul Fatawa p.536 v.7)
Only Allah Knows Best
Mohammed Tosir Miah
Darul Ifta Birmingham