I have an illegitimate child.

Answer

The biological father who has fathered a child by zina, is not accepted as the legal father by the Shariah. Thus, there are no ties of inheritance between them. The 'father' has no rights and no obligations towards his illegitimate child. The child is related to only the mother and inherits in her estate. The biological father may care for the child, educate him and provide financial support. It will be Sadqah in general.