I don't know why you end up using that exchange while people trying to avoid them, did you fall the high value of that coin in yobit than in any other exchange?
To solve your issue, the only thing you can do is, contact their support, explain all the things happened. And ask them if it's possible for you to recover your funds, but don't expect they will give you the private key of the address to recover your eth, coz obviously they will never do that.
And one thing, don't expect your problem will be solved as early as possible, yobit is known having its worst customer support, they reply mostly week(s), worst months. Only if they made their new year's resolution to improve that.
I usually double check whenever i have to make transfers, it is likely my first error that i made. But indeed i could have been much easier if yobit provided same address to client for both USDT and ETH.
According to info (Cryptoprimes) shown us here, it is veey possible for yobit to recover my funds but they are obviously not like good exchanges customer support. I am just waiting for their reply and trying all the ways to reach them, lets cooperate together and forget this exchange forever if they don't listen to their valued customers like me who have traded mostly on their pltform for millions of worth dollars but if they still don't care for their valued customers, they deserve to make their exchange a most hatered ! I will update if they ever reply ny tickets