Herzum Attachments Manager app for Jira allows to define, at project level, limits on the maximum number of attachments per issue.
This pages illustrates what you can expect when a limit on the maximum number of attachments has been configured for a project.
Assuming the following setting:
When an user try to attach more then three files to an issue that belongs to the project Sample Project, an alert appears and the fourth file is not attached to the issue.
On the issue Create and Edit screens the alert displays as follows:
On the issue View screen the alert displays as follows: