The genus Adiantum is classified under Adiantaceae by The DNA of Singapore website and The Plant List. However, based on evolutionary research, the family Adiantaceae is part of the family Pteridaceae [1]. I have decided to keep under Pteridaceae.

Reference:

1. Smith AR, Pryer KM, Schuettpelz E, Korall P, Schneider H, Wolf PG. (2006) A classification for extant ferns. Taxon 55(3): 705-731.