  We study a class of stochastic evolution equations of jump type with random
coefficients and its optimal control problem. There are three major
ingredients. The first is to prove the existence and uniqueness of the
solutions by continuous dependence theorem of solutions combining with the
parameter extension method. The second is to establish the stochastic maximum
principle and verification theorem for our optimal control problem by the
classic convex variation method and dual technique. The third is to represent
an example of a Cauchy problem for a controlled stochastic partial differential
equation with jumps which our theoretical results can solve.
