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An "exempt visa" (besides being an oxymoron) is a type of visa that shows the holder is exempt from immigration control but does not have 'right of abode' in the UK. It has no meaning outside of the UK.
I am getting exempt visa for UK. I need to know which countries I can visit there without needing any other visa?
You can visit England, Scotland, Wales, Northern Ireland, and for limited periods, Ireland and the Channel Islands and the Isle of Man.
Regarding the UK and Schengen...
Schengen is a different regime and visas issued by the UK are not fungible in the Schengen zone (and vice versa). Your Schengen application may be elevated to bona fide status because of a UK visa (or it may not), but those considerations are pure conjecture.