Users using an sdk created by swagger can use OAuth.
FusionAuth supports all of the grants listed there except "Client Credentials" (if that's an important grant to you, please vote on this GitHub issue).
That said, you can log a user in using this API: https://fusionauth.io/docs/v1/tech/apis/login#authenticate-a-user
As mentioned in that document, you can require a FusionAuth API key (information about creating this here: https://fusionauth.io/docs/v1/tech/apis/authentication#manage-api-keys ) which would not be a per user API key. Or you could disable authentication for the /apilogin endpoint:
Authentication may be disabled per Application, see application.loginConfiguration.requireAuthentication in the Application API or navigate to Applications Edit Security in the user interface.
and have users authenticate against that endpoint.
If on the other hand you are asking about application type API keys that are managed by FusionAuth, the short answer is that is not a feature of FusionAuth. Please see this forum post for other options.