What is the prefix for happily?

There isn't a specific prefix for "happily". "Happily" is an adverb, meaning it describes a verb. It comes from the adjective "happy".

However, you can use prefixes to form other words related to happiness:

* Un- - unhappy

* Over- - overjoyed

* Mis- - miserable (though not directly related to "happy", this word implies a lack of happiness)