Wireless sensor networks consist of sensor nodes that are physically distributed over different locations. Spatial filtering procedures exploit the spatial correlation across these sensor signals to fuse them into a filtered signal satisfying some optimality condition. However, gathering the raw sensor data in a fusion center to solve the problem in a centralized way would lead to high energy and communication costs. The distributed adaptive signal fusion (DASF) framework has been proposed as a generic method to solve these signal fusion problems in a distributed fashion, which reduces the communication and energy costs in the network. The DASF framework assumes that there is a common goal across the nodes, i.e., the optimal filter is shared across the network. However, many applications require a node-specific objective, while all these node-specific objectives are still related via a common latent data model. In this work, we propose the DANSF algorithm which builds upon the DASF framework, and extends it to allow for node-specific spatial filtering problems.