We propose a novel kernel adaptive filtering algorithm, dubbed Parallel HYperslab Projection along Affine Sub-Spaces (Φ-PASS), which reuses observed data efficiently. We first derive its fully-updating version that projects the current filter onto multiple hyperslabs in parallel along the dictionary subspace. Each hyperslab accommodates one of the data observed up to the present time instant. The algorithm is derived with the adaptive projected subgradient method (APSM) based on which a convergence analysis is presented. We then generalize the algorithm so that only a few coefficients, whose associated dictionary-data are coherent to the datum of each hyperslab, can be updated selectively for low complexity. This is accomplished by performing the hyperslab projections along affine subspaces defined with the selected dictionary-data. Numerical examples show the efficacy of the proposed algorithm.