Client side authentication using certificate

Hi, would like to get some advice on how to achieve the client side authentication using certificate.

We have a web application that hosts classified data, besides using a login screen to protect the content, we would restrict the access only from predefined list of clients, i.e. even if you have the username and password, as long as you are not accessing from the designated clients, you are not able to access the information.

I am not sure if there is any type of certificate we can get from Comodo to achieve the above objective, i.e. we can install the certificate on the clients which we allow the access. Clients without the certificate installed will not be able to access the server.

Appreciate any advice.