  Since symmetry properties of coherent states (CS) on M\"obius strip (MS) and
fermions are closely related, CS on MS are naturally associated to the
topological properties of fermionic fields. Here we consider CS and
superpositions of coherent states (SCS) on MS. We extend a recent propose of CS
on MS (Cirilo-Lombardo, 2012 [25]), including the analysis of periodic
behaviors of CS and SCS on MS and the uncertainty relations associated to
angular momentum and the phase angle. The advantage of CS and SCS on MS with
respect to the standard ones and potential applications in continuous variable
quantum computation are also addressed.
