Is it possible to allow the user to use Public Key and Password to authenticate to their ssh account (Have both options enabled rather just one or the other)?
If it possible, how to do so?
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As already stated in the comments password and public key authentication are enabled by default. If you enable ssh and know the name resp. ip address of the RasPi you can just connect to it with user pi and password raspberry. You can also use public key authentication out of the box. Just install public and private keys as described for ssh. You can find an example at Unable to SSH after securing Pi.
While out of the box the Pi is using passwords, and public keys in the sense of host keys, I think what he is asking is if you can continue to use password authentication AFTER you setup user public key authentication.
Once you do so, then there is no need for the less secure password authentication, and the whole point of setting that up is to not need to stop and enter a password, which can be brute force attacked to begin with.
So, there is no need to do such a thing.
Check out "SSH Mastery" by Michael W. Lucas for more detail.