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We study the magneto-conductance of a $1.4~\mathrm{\mu m}$-wide quantum dotin the fractional quantum Hall regime. For a filling factor $\approx 2/3$ and$\gtrsim 1/3$ in the quantum dot the observed Coulomb resonances show aperiodic modulation in magnetic field. This indicates a non-trivialreconstruction of the 2/3 fractional quantum Hall state in the quantum dot. Wepresent a model for the charge stability diagram of the system assuming twocompressible regions separated by an incompressible stripe of filling factor$2/3$ and $1/3$, respectively. From the dependence of the magnetic field periodon total magnetic field we construct the zero-field charge density distributionin the quantum dot. The tunneling between the two compressible regions exhibitsfractional Coulomb blockade. For both filling factor regions, we extract afractional charge $e^*/e = 0.32 \pm 0.03$ by comparing to measurements atfilling factor 2. With their close relation to quantum Hall Fabry-P\'{e}rotinterferometers, our investigations on quantum dots in the fractional quantumHall regime extend and complement interference experiments investigating thenature of anyonic fractional quantum Hall quasiparticles.

Fractional Coulomb blockade for quasiparticle tunneling between edge channels