Generally, a fellowship has to be ACGME accredited in order to get sponsored for a J1 visa.
Some specialties have only part of their fellowships ACGME accredited (e.g. radiology), some don't have any accredited fellowships at asll (e.g. ophtho).
If a specialty is recognized by the repsective specialty college, you can be sponsored for a J1 visa even in the absence of formal accreditation. There are various position statements on the ECFMG website by the different colleges defining what they consider an 'accepted' subspecialty. Some specialty colleges handle it on a case by case basis through their education committee, others just issued a blanket statement.
