Lets assume that you host your static website on Amazon Web Services S3.
Security is an important activity when it comes to hosting in cloud. You have to lock down all other access to the S3 bucket and validate access externally to S3 bucket. If you were to give access to someone to the S3 bucket, it has to be through IAM (Identity and Access Management) credentials and completely avoid sharing the AWS root credentials to AWS management console.
Cloud flare is a good service that one can use to secure the static website that's hosted on AWS S3. Cloud flare acts as a Web application firewall in this case, securing your website at application layer.
Sign up for cloudflare.com service and login to cloudflare.com. You can use the free option service to begin with, then later when your business grows you may sign up for paid services as required.
You will be requested to validate your email address first.
Pls refer to following links if you face any issues in the above process.
Happy Hosting !!!