A true fat quarter is a full yard of of 44" wide fabric cut into forths down the center length wise then down the ceter width wise yielding 4 pieces 18x22.
Almost all of my patterns that call for fat quarters say I can substitute 1/4 yrd fabric (9x44) for each fat quarter it calls for. But most of those are strip patterns and don't call for cuts larger 4 inches wide.
The cuts (size and shape) in your pattern are what dictates if you can get away with 1/4 yd cuts works well for strips or if you need 1/2 cuts needed if you have wider strips or blocks you are cutting.