Clearly we cannot predict what an unknown court might rule based upon unknown factors. However, it is possible that a court might find your residing with a convicted felon currently on parole is too great a risk.
I find it curious that he went to prison for what seems to be a first offense for theft and/or receiving stolen property. One usually goes only to county jail for that. And, if he served only a few months, that sounds as if it was a parole violation and not an original sentence. And, disorderly conduct? People don't go to prison for that. Have you actually SEEN his criminal history record? Or, are you basing your conclusions upon his statements? Keep in mind that your baby daddy will almost certainly seek to obtain the full record and maybe even related police reports and if he can show that your BF's activities or history can place your mutual child at risk, he will stand a better than even chance of wresting custody from you.
You may discover that your boyfriend's convictions and past allegations are a little more than he has let on.

