No, Zapper does not charge fees.
As a gateway to DeFi, Zapper may expose users to fees required by integrated DeFi protocols (ie traders pay 0.3% fees trading on Uniswap).
When users transact on Zapper, they do pay fees to confirm their transactions per usual on the Ethereum network or any other blockchain like Polygon. However, these fees are not collected by the Zapper platform. They are passed directly to miners who support confirming transactions. In certain instances while investing in Zapper Pools, Zapper may even help users save gas fees by bundling multiple DeFi actions into a single transaction.