We study the magneto-conductance of a $1.4~mathrm{mu m}$-wide quantum dot in 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 a periodic modulation in magnetic field. This indicates a non-trivial reconstruction of the 2/3 fractional quantum Hall state in the quantum dot. We present a model for the charge stability diagram of the system assuming two compressible regions separated by an incompressible stripe of filling factor $2/3$ and $1/3$, respectively. From the dependence of the magnetic field period on total magnetic field we construct the zero-field charge density distribution in the quantum dot. The tunneling between the two compressible regions exhibits fractional Coulomb blockade. For both filling factor regions, we extract a fractional charge $e^*/e = 0.32 pm 0.03$ by comparing to measurements at filling factor 2. With their close relation to quantum Hall Fabry-P{e}rot interferometers, our investigations on quantum dots in the fractional quantum Hall regime extend and complement interference experiments investigating the nature of anyonic fractional quantum Hall quasiparticles.
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