Damaged my superficial branch of radial nerve. muscle below looks atrophy. is it neurogenic atrophy? what are the treatments?

Yes, depends: There are roughly 3 types of nerve injury. Neurapraxia is when just the nerve sheath is damaged and has the best prognosis and is the most common. Axontomesis is when the nerve is damaged but not the sheath and has variable prognosis. Neurontmesis is when both are disrupted and has a poor prognosis generally.

Sounds like it.: Damage to the motor nerve can produce distal atrophy. If that is the case the degree of injury or severety of the damage to the nerve is the important question. Nerve injuries can range from trivial to severe. Nerves severely damaged may never develop function and nerve with less severe injury would return to function. Having atrophy mean the damages is somewhat sever and you need a neurologist.

Physical therapy: U'r treatment would involve Physical Therapy and muscle strengthening exercises. If u don't use it u will lose it to make it simple. Even if it's hard u must work through that so the atrophy does not get worse.