To ‘mint’ an NFT is to register it on the blockchain and to ascribe ownership of that file to a specific user’s wallet. Gas fees covers the cost of processing blockchain transactions.
If you are creating a custom contract, gas fees are also required to add the contract to the blockchain.
Polygon: Verisart covers the transaction fees for NFTs minted on Polygon.
Ethereum: You will need ETH in your wallet to cover the transaction fees for minting on Ethereum.