After living as a lawful permanent resident for at least 5 years (3 years if married to a US citizen), you may be eligible to apply for naturalization to become a US citizen.
Other requirements must be satisfied: good moral character (based on your criminal history, you may be prevented from becoming a US citizen, or even placed into removal proceedings), physical presence (you have to spend at least 50% of your time living in the US), continuous residence (absences from the US lasting longer than 6 months may break your continuous residence, although there may be some exceptions) are among those causing most concerns when applying for naturalization.
If you became a US citizen before your child turned 18, s/he may have automatically acquired US citizenship. The laws of derivative citizenship, however, changed a lot during the last century. Contact us directly to inquire for more information.