Question about felony and citizenship?

My cousin is a USA Legal resident and would like to be a USA Citizen but he had a felony 3 years ago and he doesnt know if he can apply. He was caught with a bottle of 30 pills without a name on his car, he explained to the police that those pills belong to his mom and she had the prescription (percocet) because his mom used it for pain due to a medical problem that right now I forgot the details, but my cousin got arrested anyway because they told him that percocet is a drug. The case was dismissed but he still has that felony that says ILL DRUGS/TRAFFICK. Does anyone know if he can still apply or he need to wait 3 years more? Thanks!