Is there a way to recover it? Or just learn from the mistake?
Wait for the support to reply you. I have seen cases where Yobit support will provide you a redeemable code equivalent to the amount of ETH you sent to their ETC wallet. So everything should be ok.
Other than there, there is nothing you can do to recover your coins as Ethereum transactions are irreversible and only Yobit can help you.
This user did the same as you and sent ETH to Yobit's ETC address.
You guys won't believe this. Yobit gave me an activation code and then a link to enter it which had gave me the full amount of my ETH from their insurance fund. WTF. Problem solved. I truly can't believe it.