  The purpose of this paper is to introduce and study the notion of generalized
Reynolds operators on Lie triple systems with representations (Abbr.
\textsf{L.t.sRep} pairs) as generalization of weighted Reynolds operators on
Lie triple systems. First, We construct an $L_{\infty}$-algebra whose
Maurer-Cartan elements are generalized Reynolds operators. This allows us to
define a Yamaguti cohomology of a generalized Reynolds operator. This
cohomology can be seen as the Yamaguti cohomology of a certain Lie triple
system with coefficients in a suitable representation. Next, we study
deformations of generalized Reynolds operators from cohomological points of
view and we investigate the obstruction class of an extendable deformation of
order $n$. We end this paper by introducing a new algebraic structure, in
connection with generalized Reynolds operator, called NS-Lie triple system.
Moreover, we show that NS-Lie triple systems can be derived from NS-Lie
algebras.
