What some people do is send their kid to a regular yeshiva and then rent a room for them from someone in the neighborhood, but rents in NYC are very expensive and this alone might cost you $500-$1000 a month depending on living conditions
I dont think Chassidic schools (except for Chabad) would take him
BTW Its not clear to me if your son needs special Ed? If he needs some sort of special ed those schools cost $50,000