  This paper is concerned with the backward stochastic differential equations
whose generator is a weighted fractional Brownian field: $Y_t=\xi+\int_t^T Y_s
W (ds,B_s) -\int_t^T Z_sdB_s$, $0\le t\le T$, where $W$ is a $(d+1)$-parameter
weighted fractional Brownian field of Hurst parameter $H=(H_0, H_1, \cdots,
H_d)$, which provide probabilistic interpretations (Feynman-Kac formulas) for
certain linear stochastic partial differential equations with colored
space-time noise. Conditions on the Hurst parameter $H$ and on the decay rate
of the weight are given to ensure the existence and uniqueness of the solution
pair. Moreover, the explicit expression for both components $Y$ and $Z$ of the
solution pair are given.
