paradoxically

adjective

1. having the nature of a paradox; self-contradictory.
2. Medicine/Medical. not being the normal or usual kind: Stimulants are a paradoxical, albeit effective, medication used for certain forms of hyperactivity.

adj.1580s, from paradox + -ical. Competing forms were paradoxal (1560s), paradoxial (1620s), but they survive in niches, if at all. Related: Paradoxically.