I can't see a project when creating a new ticket.

[Junting Lu]

I've been told that I have all the permissions, but there is a project that I am unable to see in the project dropdown when creating a new ticket. I can however see the project's issue board...

[Nic Brough -Adaptavist-]

If you can't see the project, you do not match the rule for "can browse project" in the permission scheme.

You need to get that checked with your JIRA administrators.   It sounds like they could be making incorrect assumptions - get them to show you the project permission scheme, which should tell you why you don't match.