  In this paper, we consider a class of stochastic control problems for
stochastic differential equations with random coefficients. The control domain
need not to be convex but the control process is not allowed to enter in
diffusion term. Moreover, the terminal cost involves a non linear term of the
expected value of terminal state. Our purpose is to derive a new version of the
Pontryagin's stochastic maximum principle by adopting an idea inspired from the
work of Peng [S. Peng, Maximum Principle for Stochastic Optimal Control with
Nonconvex Control Domain, Lecture Notes in Control & Information Sciences, 114,
(1990), pp. 724-732]. More specifically, we show that if we combine the spike
perturbation of the optimal control combined with the stochastic Feynman-Kac
representation of linear backward stochastic partial differential equations
(BSPDE, for short), a new version of the stochastic maximum principle can be
derived. We also investigate sufficient conditions of optimality. In the last
part of this paper, motivated by our version of SMP, an interesting class of
forward backward stochastic partial differential equations is naturally
introduced and the solvability of such kind of equations is briefly presented.
