quantum wire with spin-orbit interaction (SOI) placed under a Zeeman field and in proximity to a bulk superconductor,[@Sau2010; @Alicea2010; @Lutchyn2010; @Oreg2010] in cold atoms in optical lattices with effective gauge fields generated by spatially varying laser fields,[@Sato2009] bilayer electron gases in semiconductor heterostructure with interlayer Coulomb coupling,[@Nakosai2012] among others. Several groups of experimentalists have recently reported that they have observed the signatures of Majorana fermions appearing at the ends of nanowires attached to superconductors.[@Mourik2012; @Rodrigo2012; @Deng2012; @Rokhinson2012] For a review we refer to Ref. .

The effect of spatial inhomogeneity on a superconducting quantum wire has been a nontrivial problem.[@Motrunich2001; @Gruzberg2005; @Brouwer2011; @Lutchyn2012; @Lobos2012; @Bagrets2012; @Takei2012; @Adagideli2013; @Sau2013] The energy distributions of the end states have been obtained for the Dirac equation with random mass and a 1D spinless superconductor.[@Brouwer2011] The interplay of disorder and correlation in 1D TSs has also been investigated.[@Lobos2012] Among the possible realizations of spatial inhomogeneity, quasiperiodic (Harper) potential modulation forms a special class in that in 1D system all the single particle eigenstates become localized at the same modulation strength. Quasiperiodic potentials have been experimentally studied in optically trapped cold atom systems [@QuasiperiodicColdAtoms] as well as in solid state, misfit compound [@1301.6888] systems. Signatures of 