I want to support HTTPS in my web application. Since the certificates from Verisign are costly, I decided to use openssl for generating certificate. Here is the link I referred https://community.jboss.org/wiki/JBossAS7ConfiguringSSLOnJBossWeb
When I tried to access the application in browser I got the error “The site’s security certificate is not trusted”. Here is the screenshot,

Please let me know how I can solve this error? Is it possible to use openssl in production?
The issue is that your self signed certificate is not ‘trusted’ by the browser. It does not recognise it as signed by one of the certificate authorities it trust.
You have two options – tell the browser it can trust the certificate or tell the browser that it can trust the entity which issued it (meaning that if you use the same certificate to sign other certificates; that those also get trusted).
See http://googlechrometutorial.com/google-chrome-advanced-settings/Google-chrome-ssl-settings.html for more information. Once you are in ‘Manage certificates’ you can import your own ones.
Every browser, every users, will have to go through those steps. So that is practical logistical limit on how much ‘production’ you can run with this.
Do check out the various ‘free’ certificates; they are very low cost.