Ok, I'll probably have to see a dermatologist since dandruff shampoos don't work.
Looks like a psoriatic plaque, from the localization, and the spillage below the scalp border, however it could be Seborrheic dermatitis, a severe form of dandruff.
It doesn't itch either. Just looks gross.
I've tried using regular shampoo with no results.
You may be reacting to the shampoo you use so you could ask your pharmacist what other shampoo might be of help but have a more mild effect. If that doesn't help improve things then it would be worthwhile to see a dermatologist.