The phrase "in a timely fashion" is correct and can be used in written English. You can use it to describe when something should be done or completed, such as in the following example: I will complete the project in a timely fashion.
"It reimburses doctors in a timely fashion".
Tickets to be booked in a timely fashion".
Most leave in a timely fashion, officials said.
"So we have to do it in a timely fashion".
"Can you get the examination in a timely fashion?
Eggs, coffee and check came in a timely fashion.
Bonnick said: "It's the bench's view that this application was not made in a timely fashion".
Thanks to Ludwig my first paper got accepted! The editor wrote me that my manuscript was well-written
Listya Utami K.
PhD Student in Biology, Bandung Institute of Technology, Indonesia