Methane (CH4) is one of the most significant greenhouse gases responsible for about one-third of climate warming since preindustrial times, originating from various sources. Landfills are responsible for a large percentage of CH4 emissions, and population growth can boost these emissions. Therefore, it is vital to automate the process of CH4 monitoring over landfills. This study proposes a convolutional neural network (CNN) with an Atrous Spatial Pyramid Pooling (ASPP) mechanism, called PRISMethaNet, to automate the CH4 detection process using PRISMA satellite data in the 400-2500 nm spectral range. A total number of 41 PRISMA images from 17 landfill sites located in several countries, such as India, Nigeria, Mexico, Pakistan, Iran, and other regions, were used as our study areas. The PRISMethaNet model was trained using augmented data as the input, and plume masks were obtained from the matched filter (MF) algorithm. This novel proposed model successfully detected plumes with overall accuracy (OA), F1-score (F1), precision, and recall of 0.99, 0.96, 0.93, and 0.99, respectively, and quantification uncertainties ranging from 11 % to 58 %. An unboxing of the ASPP module using Gradient-weighted Class Activation Mapping (Grad-CAM) algorithm demonstrated a strong relationship between larger dilation rates (DRs) and CH4 plume detectability. Importantly, the results highlighted that plume masks obtained by PRISMethaNet provided more accurate CH4 quantification rate compared to the statistical methods used in previous studies. In particular, the mean square error (MSE) for PRISMethaNet was approximately 1,102 kg/h, whereas the MSE for the commonly used statistical method was around 1,974 kg/h.