I don’t believe this is possible yet in osTicket. Tasks are a relatively new feature, and it may be that they are still developing it.
osTicket Core v1.15 was released just yesterday. I haven’t had a chance to play with it yet, or even to read it’s release notes. If the ability to add new columns in the Tasks table has been added, that means it will appear downstream in an osTicket Awesome very soon.
Failing that, the only other suggestion I can think of is to ask your question in the osTicket forums. I rather doubt it, but perhaps there is something that I have overlooked.