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In this study topological properties of static and dynamic  Su-Schrieffer-Heeger models with staggered further neighbor hopping terms  of different extents are investigated. Topological characterization  of the static chiral models is established in terms of  conventional winding number while Floquet topological character is  studied by a pair of winding numbers.  With the increase of extent of further neighbor terms topological phases  with higher winding numbers are found to emerge in both static and dynamic  systems. Topological phase diagrams of static models for four different  extents of further neighbor terms are presented, which has been generalized  for arbitrary extent afterwards. Similarly, Floquet topological  phase diagrams of four such dynamic models have been presented.  For every model four different parametrizations of hopping terms  are introduced which  exhibits different patterns of topological phase diagrams.  In each case emergence of `0' and `$\pi$' energy edge states  is noted and they are found to consistent to the  bulk-boundary correspondence rule applicable for chiral topological systems.

Floquet topological phases of higher winding numbers in extended Su-Schrieffer-Heeger model under quenched drive