  We have studied the exact solution of the extended cluster compass ladder,
which is equivalent to extended quantum compass model with cluster interaction
between next-nearest-neighbor spins, by using the Jordan-Wigner transformation.
We show that this model is always gapfull except at the critical surfaces where
the energy gap disappears. We obtain the analytic expressions of all critical
couplings which drive quantum phase transitions. This model shows a rich phase
diagram which includes spin-flop, strip antiferromagnetic and topological
ordered on the legs, in addition to the phase with antiparallel ordering of
spin y component on the rungs. We study also the universality and scaling
properties of the three point correlation functions derivatives in different
regions to confirm the results obtained using the energy gap analysis. On the
other hand, we have replaced the cluster interaction with usual form and using
the Lanczos method a numerical experiment is done. Analyzing the numerical
results, we show that the effect of the cluster interaction between
next-nearest-neighbor spins is completely different from the usual form.
