Modishly is the adverb of modish: in a modern, fashionable way. Someone dresses modishly, a room is modishly decorated, an idea is modishly put. The feel is the same as modish — a little formal, a little old-fashioned, more at home in writing than in chat. Though actually, if you say it aloud to friends, they may hear modestly by mistake, which is a very different word (in a quiet, not-boastful way). In speech people would more often say fashionably or “in a trendy way.”