Without knowing your custom neural network model, it is not possible for us to understand how it can be used to train new data set. However, you can basic workflow from the following example which shows how to classify new image data by fine tuning the existing, pretrained neural network.
https://www.mathworks.com/help/releases/R2017a/nnet/examples/transfer-learning-and-fine-tuning-of-convolutional-neural-networks.html
Since this is an example from Neural Network Toolbox, you need to have Neural Network Toolbox license to use some of the functions, but it can be used to learn some of the existing workflows.
