Sent a large amount of USDC.e to AVAXC on Binance.

Hey everyone, I've fucked up really badly. Saw that Binance accepted USDC on AVAXC, but didn't know that there are TWO USDCs on AVAXC, so I sent USDC.e instead. Sent an appeal to retrieve the USDC.e but was rejected and they only said, "Dear User, USDC.e token deposit using AVAXC network we are unable to retrieve. Please be reminded to check the token and network next time. Thank you."

Problem is this is a huge chunk of my portfolio, I live in a third world country, and I don't what I'm going to do with this money gone. Another thing I don't understand is, don't they own that private key? It must be possible to retrieve. If it is just the gas fee I'm willing to pay 100s of dollars to get this back. Please help.