QTimer cannot suspend a running process at an arbitrary point, service another interrupt, and then resume where it left off: this is low-level and real time operating system stuff typically.

It really does not make sense to attach a process that never returns or takes longer than the timer period (you do both) to a timer that fires every 100 or 1000 milliseconds. If the processes are processing queues of repetitive short processing steps then a simple redesign of what is done in response to a timeout may suffice (you might then use QtConcurrent or feed a queue to a worker thread).