Due process is a doctrine that is applied to criminal court, not civil court. So this is being used improperly. However regardless, assuming you did not lose all parental rights, someone in your situation should have been served with any paperwork re: the child's legal status. Even if you were incarcerated.
Someone in your situation at this point can file a suit to modify the existing custody of the child. While the fact that you were not served can be argued to reverse a decision, the Court will still base the final (reconsidered) decision in the "best interest of the child." You may be able to get visitation.
The Court decides on custody based on the rule of thumb of "best interest of the child." This includes, but is not limited to, general stability of the person, financial stability, indoctrination of the child in the current school and environment, household condition and living condition of the child, other persons living in the house, etc. Even if a parent does not get managing custody, they are almost guaranteed visitation unless they have a drug problem, alcohol dependency, or an unsafe home environment. Abuse and or neglect of the child or previous children are an almost automatic bar for even visitation, although supervised visitation may be granted by the Court.
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