On iPads, button-press protocols (Yubico OTP, static password, etc.) WebAuthn (FIDO U2F and FIDO2), and OATH (Yubico Authenticator) work. PIV also works over Lightning and NFC, but not over USB-C. OpenPGP does not work at this time.
In practice, although the above listed protocols are supported, whether a YubiKey will work for a given service on an iPad typically depends on the service itself. Generally speaking, Yubico recommends consulting documentation provided by the service provider, which can often be found via the Works With YubiKey Catalog, or simply testing for functionality.
In the event that something is not working, we would encourage you to reach out to Apple, the service provider, or us via https://yubi.co/support, depending on where the fault lies. If you are not sure, feel free to open a ticket with us via https://yubi.co/support, and we will assist with narrowing down the cause of the problem.
Please see here for further information regarding use of YubiKeys with iPads.