In a manner characteristic of a baby; in a childish, immature, or silly way.
From babyish (baby + -ish meaning 'having qualities of') plus the adverb-forming suffix -ly. This straightforward construction follows standard English patterns for turning adjectives into adverbs.
The way English turns 'baby' into 'babyish' and then into 'babyishly' shows how we stack suffixes—each one adds a layer of meaning, so by the end you've got a word that means 'in an immature manner.'
Complete word intelligence in one call. Free tier — 50 lookups/day.