I've not done it, so I don't know where to look. You'll need to find the files that draw the menu and suppress it (bearing in mind you need to think about whether you want to cripple it globally or just for a set of projects). Then you'll need to think about all the other places you can create sub-tasks from.
You can disable it by disabling the relevant plugin component.
If you spend enough time as a Jira admin - whether you are managing a single, mid-sized instance, a large enterprise one or juggling multiple instances at once - you will eventually find yourself in ...
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