Hi @Mathew Kuruvilla and welcome to the Community!
I am assuming that you have created Project bug as a sub-task issue type in Jira Settings > Issues > Issue Types?
If so, note that you can indeed make this available in a project, as long as your project is company managed. You cannot add a centrally managed issue type to team managed projects. If you need that, you would need to create the issue type again in the project itself.
But to come back to a company managed project: to make the new issue type available in a company managed project, you would need to add it to the issue type scheme associated with your project. The easiest way to find out what that is, navigate to project settings in your project, and then select Issues > Types. You will be able to click the Actions button near the top right of your screen and then select Edit issue types. You should be able to locate the new issue type and add it to the scheme. Don't forget to save your changes there ...
On a final note: issue types in company managed projects are quite fundamental to your (project) configuration. The screens and workflows in your project are linked to the issue types you set up, so you may also need to look at additional settings there to make sure everything is set up properly for the new issue type.
Hope this helps!
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