  We consider tunneling through two point contacts between two edges of Quantum
Hall liquids of different filling factors $\nu_{0,1}=1/ (2m_{0,1}+1)$ with
$m_0-m_1\equiv m>0$. Properties of the antidot formed between the point
contacts in the strong-tunneling limit are shown to be very different from the
$\nu_0 =\nu_1$ case, and include vanishing average total current in the two
contacts and quasiparticles of charge $e/m$. For $m>1$, quasiparticle tunneling
leads to non-trivial $m$-state dynamics of effective flux through the antidot
which restores the regular ``electron'' periodicity of the current in flux
despite the fractional charge and statistics of quasiparticles.
