Does the surname arya comes under schdeule caste?

Arya does not belong to any caste or category. So anyone is free to add Arya.

The Aryans were considered to be a valiant, superior and civilised . Arya means cultured, refined and righteous person.

Arya became a popular Word when Swami Dayanand Saraswati founded Arya Samaj (superior society) in early 19th century. He ridiculed the rituals dominated worship and opposed idol worship. His sect became popular and his followers started adding Arya after name to sound distinct from orthodox Hindus.