In general the verb "to feel" will take an adjective (happy, sad, good, bad, angry, relieved)

after it to indicate the feeling, rather than an adverb.

Assuming you're talking about a situation where something bad has happened to your friend, and you're saying you feel unhappy on their behalf, then

"I feel bad for you" is correct.

 The word "badly" can be used as an intensifier, so

 "I feel badly in need of a drink" means that you really really need one.

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