Electron Spin Resonance (ESR) can microscopically probe both conduction electrons (ce) and local moment (LM) spin systems in different materials. A ce spin resonance (CESR) is observed in metallic systems based on light elements or with enhanced Pauli susceptibility. LM ESR is frequently seen in compounds with paramagnetic ions and localized d or f electrons. Here we report a remarkable and unprecedented ESR signal in the heavy fermion (HF) superconductor beta-YbAlB4[1] which behaves as a CESR at high temperatures and acquires characteristics of the Yb3+ LM ESR at low temperature. This dual behavior in same ESR spectra strikes as an in situ unique observation of the Kondo quasiparticles giving rise to a new ESR response called Kondo coupled resonant mode (KCRM). The proximity to a quantum critical point (QCP) may favor the observation of a KCRM and its dual character in beta-YbAlB4 may unveil the 4f-electrons nature at the QCP.