I faced this issue through out last month because I had some USDT in my wallet but it was an ETH-chain USDT which requires me to have some ETH to spend as gas fee. First, I bought some Ethereum on the MEXC exchange because they had some low fee of withdrawal and a little amount as minimum withdrawal limit.
After I withdraw to my wallet, I tried to swap the USDT to ETH but I got charged $9 worth of ETH meanwhile the USDt faild to swap. After Iost $9 due to the fail swap, I was only left with $5 worth of Ethereum which was very small compare to the required gas fee to carry out the transaction.
First what I did then was to wait till early morning, once it's around 1AM-5AM gas fee usually reduces, although not all time, so you can try carrying out your withdrawal around early hours of the day.
Second suggestion is that, some wallet usually have a high transaction fee compare to other wallet, so I would suggest for you to download Metamask, import your wallet there and try using it to withdraw your coin. The wallet usually have a low fee and you can modify the fee to your choice.
It was this two method that helped me to finally move out my USDT from my wallet.