This is exactly what Smart Objects are for!
Create your "master layer" (which can consist of several layers, provided they are all selected when you do the next step).
Make it a Smart Object using Filter > Convert for Smart Filters, the layers panel flyout menu ("Convert to Smart Object") or Layer > Smart Objects > Convert to Smart Object. (There are always multiple ways to do things in Photoshop!)
[Alternatively, you can Place (File > Place) a PSD in a new Photoshop document. The external PSD will come in as a Smart Object with Free Transform active, so you can accept it as it is or resize according to what you need.
Copy this Smart Object layer using Ctl/Cmd-J or Layer > New > New Layer via Copy. It's important to copy the layer rather than making a new Smart Object.
Place the copies where you need them to be.
To change all of them at once, double click on any layer in the set, make your changes in the separate .PSB file that opens up, then save those changes and close the .PSB.