Jokily is the adverb: you do or say something in a jokey way. He smiled jokily. She jokily pretended not to know. It tells you how someone spoke or acted — not seriously, trying to get a laugh, or at least to keep the tone light. Though actually, most people say jokingly, not jokily. Jokily is real English, but it is the quieter sister; if you use jokingly, nobody will blink. Jokily can sound a tiny bit more like “in that jokey manner,” the style of the joke, where jokingly often just means “I do not mean this for real.” Neither word is formal. For a student, jokingly is the one that will sound natural almost every time; jokily is the one you may meet in writing and should still understand.