In order to server assets in Production environment; assets are first compiled and put into /public/assets directory. So, first you need to run the following command to compile the assets.
RAILS_ENV=production rails assets:precompile
It is encouraged to serve static content using NGINX/Apache. But if you want rails to serve the contents add/modify the following line on production.rb
config.public_file_server.enabled = true
In case you are facing anomaly and confident your code is correct then try clearing the cache using