Can we configure Certificate-based Authentication to connect(logon) sql client? Can we configure Certificate-based Authentication to connect(logon) sql client? or any other method to connect sql client using mutual authentication(sql server and sql client)?
Answer originally provided in a comment by Kin:

The answer is no.

Only Database Mirroring and Service Broker connections can authenticate using certificates.

You might want to check Remus Rusanu 's answer on Stack Overflow and his article:

How does Certificate based Authentication work?.