This paper primarily discusses the linear quadratic optimal control problem for discrete-time stochastic systems with indefinite control weights and constraint and Markovian jumps. We use the Karush-Kuhn-tucker (KKT) theorem basically in this paper. It is testified that the well-posedness and the attainability are equivalent about the stochastic linear quadratic optimal control problem with Markovian jumps. Furthermore, the solution of the generalized difference Riccati equation (GDRE) can indicate an optimal control.