In recent years, there has been a growing interest in time series forecasting, particularly on quantifying the uncertainty in neural model predictions using prediction intervals. This study utilizes the Joint Supervision (JS) method to construct prediction intervals, a technique that has consistently outperformed similar approaches. The JS method employs a neural network with two outputs representing the interval's boundaries and another the specific prediction. Each output is optimized with a unique loss function, incorporating tunable parameters. This work introduces a modified version of the JS (JSM), which enhances in an average 8% improvement in coverage probability while maintaining a similar or slightly greater average width. Furthermore, this research compares the JSM method implemented with both Long Short-Term Memory (LSTM) and Transformer architectures. Experiments conducted on three different databases reveal that JSM with the Transformer outperforms the LSTM version, with an average 1.77% increase in coverage probability and 12% narrower intervals.