@OP, to avoid that confusion, you better leave that wallet, it is not yours, you are not in control of that and if you keep using that wallet, you are just feeding these scammers.
As far as I understand from your explanation, this wallet is also used by others? If such a situation exists and is used by hackers, it can take serious trouble. Or by constantly checking the account, which I definitely do not recommend, it can transfer the contents of the wallet to their own accounts.
You guys better read the thread or atleast the OP before making any posts because he is talking about exchange's wallet not his own. He can't able to withdraw his balance which is showing on the exchange balance but actually there is nothing left in his wallet address so most likely he deposited into a scam exchange so there is no possible way to access those funds.
Thank you for the explanation gyus, I will try to summarize the issue here, since there is a number of posts here and people seem to read only part of it.
When I sign into the account on the particular exchange and I check the wallet there, I see remaining ETH in the amount of 0.19... However, when I check the wallet's address on a website like blockchain.com, I see the remaining ETH amount is 0.000084 (I am not sure now, because I do not want to sign into the account anymore, just in case). Also, it is showing transactions which I did not make, these transactions are not shown in the exchange's website, when I click the wallet and check transactions. These are only shown on blockchain.com.
Now when I try to withdraw the remaining ETH (shown on exchange amount 0.19...), it changes the status to frozen, there is a transaction with the status of "checking" for several hours, I think it is about 10-12 hours and after that it gets refused and the ETH just returns to the wallet (probably because that is not the actual amount that is in the wallet according to blockchain.com).
I tried to be brief, so I am not sure if I caught the bulk of the problem in this but everyone should read the whole topic in case of their interest.
I will try what you guys adviced, to create a personal wallet through metamask and withdraw to that wallet, however, I doubt it will work but I am very grateful for your advices.