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Avoid depositing the funds they asked you for because most unknown scam exchanges use these tactics to drain more money from the victim. Eventually, they will ban your account, and you won't be able to withdraw any deposits you made. I am sad about your loss. However, it would have been better to research before using any CEX, as many exchanges have recently appeared to deceive investors in conjunction with halving events.
Halving moments like now are indeed an opportunity for scammers to deceive many new users and lead them to phishing websites to start draining users' money.
They even spread feeds via email, telegram and various kinds of social media so that early adopters are interested in clicking and logging in.
For truly trusted CEXs such as Binance CEX tier etc., the fees charged will take from the amount of funds available, so there is no need to prepare fees anymore because it has been deducted by the amount of funds to be taken, so there are no coins left.
But if it still requires additional fees and even requires a 2x fee for all withdrawals, be careful with the scheme.
I also don't really understand about the 10k and 20k costs that OP meant, it seems that it does need a detailed explanation.