  Here we report on fabrication and low temperature magnetotransport
measurements of quantum point contacts patterned from a novel two-dimensional
electron system - CdTe/CdMgTe modulation doped heterostructure. From the
temperature and bias dependence we ascribe the reported data to evidence for a
weakly bound state which is naturally formed inside a CdTe quantum
constrictions due to charging effects. We argue that the spontaneous
introduction of an open dot is responsible for the replacement of flat
conductance plateaus by quasi-periodic resonances with amplitude less than
2e^{2}/h, as found in our system. Additionally, below 1 K a pattern of weaker
conductance peaks, superimposed upon wider resonances, is also observed.
