This study investigates the capability of a deep learning approach, employing a multi-head attention mechanism within a deep neural network (DNN) framework, aimed at refining the bias correction and downscaling process for the fifth generation European Centre for Medium-Range Weather Forecasts reanalysis rainfall datasets to provide local-scale daily rainfall data across Taiwan, a mountainous subtropical island. Leveraging gridded 5-km daily rainfall observations across Taiwan, the proposed DNN model, the Encoder-Decoder with multi-head Attention for auxiliary channels (EDA) model, can adeptly correct biases and downscale rainfall statistics from coarse-resolution reanalysis data by incorporating auxiliary inputs, such as surface wind information, and invariant data, such as high-resolution topography data. Our evaluation, centred on the distinct seasonal rainfall characteristics of Taiwan, uses mean rainfall patterns, rainfall statistics, extreme climate indices, and their interannual variation for the rainy seasons. The findings show the EDA model's ability to correct for overestimated low-intensity rainfall and inaccurately positioned orographic rainfall in reanalysis datasets, achieving better accuracy than conventional quantile-mapping methods. Further analysis reveals the critical role of auxiliary information of surface winds used by the EDA to enhance the downscaling accuracy across various performance metrics. This study underscores the significant potential of DNN architectures for statistical bias correction and downscaling in regions with complex terrains, by effectively integrating auxiliary data to capture the interplay between synoptic and local circulations influenced by topography.