The Month of Quarter function is supported, returning an integer 1-3, the number of the month in a given quarter. When dragging a Month of Quarter into a variable, the following tree element is created.
Variable Creation > Input > Variables: SQL Elements pane - Calendar > Month Of Quarter
Columns and/or other expressions that resolve to a date can be moved over the (empty) branch of the tree.
There are no special properties for the Month of Quarter function.