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Automated characterization of galactic substructure is an essential step in understanding the transformative physical processes driving galaxy evolution. In this study, we investigate the application of deep learning (DL) frameworks to characterize different galactic substructures hosted within parametric light-profile subtracted ``residual'' images of a large sample galaxies from the CANDELS survey. We develop a supervised Convolutional Neural Network (CNN) and unsupervised Convolutional Variational Autoencoder (CvAE) and train it on the single-Sérsic profile fitting based residual images of $10,046$ bright and massive galaxies ($H<24.5\,{\rm mag}$ and $M_{\rm stellar} \geq 10^{9.5}\,M_{\odot}$) spanning $1<z<3$, in conjunction with their visual-based classification labels indicating the nature of residual substructures hosted within them. Using our unique data preprocessing approach, we prepare our residual images such that the inputs to our DL networks comprise only ``galaxy of interest'', and augment them such that our sample span uniformly across different residual characteristics. We assess the latent space of the CNN and CvAE using Principle Component Analysis (PCA) along with independently quantified metrics of residual strength (significant pixel flux $SPF$, Bumpiness, and Residual Flux Fraction). We also employ an unsupervised Gaussian Mixture Modeling (GMM) based clustering scheme with Support Vector Classification (SVC) to identify groupings in PCA space that correspond to similar residual substructure. We find that our supervised CNN latent features in PCA space correlate with the $SPF$ values and distinguish between qualitatively strong and weak residual substructures. While our unsupervised CvAE latent space also correlates with visual and quantitative residual characteristics, but lacks clear discriminatory power when characterizing different residual substructures.