Creating child tickets from an open ticket is not an existing feature in the product. However, if the ticket you are attempting to make is somewhat predictable, I've had success with using Action Rules to achieve this. If you make a Ticket Custom Field that looks like the following *as an example*:
Label - Create Child Ticket?
Type - Single Choice
Options - Yes;No
You could have an Action Rule pick up on a ticket update with the Ticket Custom Field for 'Create Child Ticket?' answer Yes, and the Action could be to add a Task to that ticket inheriting just a few details.
I hope this helps!