아는가요 is correct. In 아는가요, 는가(요) is another suffix. It is not same to (으)ㄴ가(요)/나(요). -는가(요) is used when asking about present situation formally.(old-fashioned, not common nowadays) e.g. 지금 뭐 하는가요?(formal) = 지금 뭐 해요?(informal) 이것을 아는가요?(formal) = 이것을 알아요?(informal) In colloquial language, ~나요 is commonly used instead of ~ (으)ㄴ가(요) with adjective. ~고 싶나요 = ~고 싶은가요 어렵나요 = 어려운가요

'아는가요' is grammartically wrong. It should be '아나요'.