illegal alien toapply for green card

The alien likely should review his facts and options with an attorney. There may be something in his particular facts that give him legal options.

From the facts given, he likely has at least two major problems: a felony conviction with a long time in prison; unlawful entry and presence.

It is hard to give a specific answer with the information given. But depending on the lawfulness of his original entry into the US, and the type of felony conviction, and of course whether he has a way to adjust status now (perhaps the child is over 21, perhaps he is now married to a USC, etc.) he may be eligible for a waiver (e.g. under 212(c)) that would "forgive" the felony conviction.

Immigration is highly technical. You have to meet very narrow statutory requirements. Thus there is seldom a "general" way to apply for a green card for a person in this alien's situation.

Most importantly - don't file anything without consulting a competent attorney. It is likely that doing so will only result in the commencement of removal proceedings.