Actually an exchange is a place of buying and selling bitcoin, so definitely there is no fake bitcoin in the market circulation, people might have earned it by trading or purchased it using their debit card from fiat currency, so there's no way a fake coin could be purchased on exchange. Moreover, if its actually fake, blockchain has an explorer that reveals all bitcoin balance shown on the address which makes every transactions to be transparent, easy and accessible.
And also beware of exchange that lied to investors, some provides fake volume and liquidity which were proven to be faked at last, so if you really want a good exchange that won't give a lie about them, you could consider binance, huobi, okex and other top exchange as directed by coinmarketcap.