Touchscreens provide a platform for adaptable and versatile user interfaces making them a popular choice for modern smart devices. However, touchscreens lack physicality. Existing solutions to add tangible user interfaces to smart devices often require complicated assembly or occlude part of the touchscreen. We propose ClipWidgets: 3D-printed modular tangible UI extensions for smartphones. ClipWidgets uses a conical mirror and a custom phone case to redirect the field of view of the rear camera of a smartphone to the phone's periphery. This allows the phone to optically sense input from modular passive 3D-printed widgets that are attached to the phone case. We developed three different widget types (button, dial and slider) that require minimal calibration and minimal assembly. To demonstrate the functionality of ClipWidgets we used it to prototype three different applications: a game controller, a music interface and an interactive graph tool.