Is the AWS Cognito right service here or I need different AWS service

There is a mobile app that uses OpenID Connect for SSO. That mobile app is not built with AWS. Developers of that app are asking me to provide my own SSO authentication service with OpenID Connect that they can use it for user authentication in that app.

My question is: Does the AWS Cognito right tool to built my own SSO service with OpenID Connect that will suit well for the case described above? Or I need different AWS service?