It appears that you are eligible for citizenship based on your family history. Ive included the law for you below. However, you really need to have a consultation with an immigration attorney to go through your criminal record and also verify specific dates in connection to your N-600. A lot of us offer free consultations so please reach out.
A child born outside of the United States to two foreign national parents, or one foreign national parent and one U.S. citizen parent who subsequently lost U.S. citizenship, acquires citizenship under former INA 321 if:
The child’s parent(s) meet one of the following conditions:
*Both parents naturalize;
*One surviving parent naturalizes if the other parent is deceased;
*One parent naturalizes who has legal custody of the child if there is a legal separation of the parents; or
*The child’s mother naturalizes if the child was born out of wedlock and paternity has not been established by legitimation
The child is under 18 years of age when his or her parent(s) naturalize; and
The child is residing in the United States pursuant to a lawful admission for permanent residence at the time the parent(s) naturalized or thereafter begins to reside permanently in the United States.