Outlook rule for a specific period date

You can do this, but you'd need to update the rule every quater

When you create a new rule, there is the option in Step 1

received in a specific date span

That will allow you to chose the date range you want to work with. In step 2 you can then choose

move to the specified folder

As per your comments, I'd probably create the sub folder now, similar to

2016
    Q3
    Q4
2017
    Q1
    Q2
    Q3
    Q4
2018
    Q1
    Q2
    Q3
    Q4
2019
    Q1
    Q2
    Q3
    Q4

And then (using the example above) create the rules required! This way you won't have to think about it until 2020!!