  In this article, we have constructed an interesting type of generalized
Schottky group, named as Fuchsian Schottky group of arbitrary finite rank, in
the context of the classical Schottky group (i.e., Schottky curves which are
Euclidean circles). After that, we initiated the construction of the
generalized Fuchsian Schottky group of any finite rank by including
orientation-reversing isometries of the hyperbolic plane as side-pairing
transformations. Further, we have investigated the hyperbolic ends for any
arbitrary finite rank Fuchsian Schottky groups from the point of view of the
Euler characteristic in the hyperbolic surface. Finally, we have shown that the
compact core of the conformally compact Riemann surface can be decomposed into
non-tight pairs of pants by using suitable twist parameters with some fixed
Bers' constant. The Fenchel-Nielsen coordinates for Teichm\"uller space
corresponding to any finite rank Fuchsian Schottky groups are also obtained.
