I told you many times that a very exact assessment can only be made by your lawyer or by an experienced consultant who really works with you personally and knows your situation in detail, which includes necessarily reading of all official letters you get from Ausländerbehörde, BAMF etc. I don't quite understand what you mean by "cancelling your illegality" - probably that the investigating procedure was stopped ("eingestellt") by the Staatsanwaltschaft.
If you haven't got any letter with a claim for penalty until now and the Staatsanwaltschaft has informed you about stopping the investigation procedure for a case of your illegal staying, you mustn't worry about that. And if you didn't have other criminal cases, the criminal story can't be a reason for a rejection.
The Ausländerbehörde can bring the argument that you came to Germany without a proper visum as a reason for a rejection, even if the Staatsanwaltschaft didn't give you any penalty. These are different things. The Staatsanwaltschaft has to do with the criminal law and the Ausländerbehörde with the Alien law, which generally claims for a proper visum procedure and a passport for issuing a residence permit. In your case the exclusion can be done (and is often the case), because of the interest of the child. Only there is no guarantee.
Please ask your lawyer or a councelling center to explain your situation, because I can only explain how the things work generally.