You might have to go back and try to determine the cause. There are at least three causes for this common behavior.

Attention - If he has gotten attention for it, even if it is "adverse" attention, he might be continuing to do it for the attention. This is common with other forms of self-injury, but not so much with nail-picking. (ASD kids tend not to separate "good" attention from "bad" attention.

Stress - Sometimes an ASD kid will nail-pick to get their mind off the stress of the moment. It may take a while to figure out what they are stressed about, because it might be something unrelated, such as potty training (for younger kids) or a new schedule at school.

Repetitive Behavior - Many "stims" get a life of their own, and self-injury can be a frightening one to watch. ASD kids do it to help them deal with their world, and to feel more control over the situation. Oddly, stims can be a way to calm down. A good therapist might be able to redirect this into a more harmless behavior.

My son is constantly biting his nails and around his fingers. I bought him a fidget called tangle relax therapy. He uses this now to chew on. I know you said your son is picking his nails, but maybe a fidget toy can help him keep his hands busy instead of picking on them. I hope you'll find something soon that can help him.

So, if I understand...he is picking his nails with his hands. He doesn't put his hands in his mouth at all. Then, he may be seeking stimulation for his hands. Here are some things we tried: play with small toys in bins filled with dry rice, sand or dried beans; hide small objects in playdough, put shaving cream on a tabletop and let him fingerpaints; use short pieces of crayons and pencils that are more challenging to grasp.

Our older NT son does that. He does have iron deficiency that we are addressing and we are also looking into a supplementing NAC which has been shown to reduce some ASD symptom (double blind study) and may help with nail biting according to a few published case studies. He doesn't bite his nail either but there is definitely some sensory seeking behaviour here.

Is it oral stimulation he's seeking or does he need something for his hands?