Some of the most commonly used signatures are symmetric.
If two parties have a shared secret (a random value), then as a signature they can use the hash of the combination of the message and the key. To verify the signature, the other party generates their own signature for the message and then checks that both signatures match.
This is the principle of the HMAC-SHA256 signing algorithm used for most JSON Web TokensTokens, e.g. for OIDC authentication with federated online identity providers. It is also the basis of AWS SigV4 protocol, for signed requests used to authorise any control of resources across some of the largest cloud datacentres.