We designed disk patch resonators to meet the requirements for enhanced coupling of optical cavities to intersubband transitions in heterostructures in the terahertz frequency regime. We applied modifications to the standard patch resonator in the form of a chain of holes and slits to control the resonator eigenmodes featuring quality factors ωFWHM/ω0 as high as 40. Due to the broken rotational symmetry of the resonators the individual eigenmodes can be accessed selectively depending on the incidence and the polarization of the THz wave. The demonstrated post-process blue-shifting of the resonance frequency up to 50% is a key tuning knob for an optimization of light-matter interaction in a quantum system.