The human brain functions very differently from artificial neural networks (ANN) and possesses unique features that are absent in ANN. An important one among them is "adaptive synaptogenesis" that modifies synaptic weights when needed to avoid catastrophic forgetting and promote lifelong learning. The key aspect of this algorithm is supervised Hebbian learning, where weight modifications in the neocortex driven by temporal coincidence are further accepted or vetoed by an added control mechanism from the hippocampus during the training cycle, to make distant synaptic connections highly sparse and strategic. In this work, we discuss various algorithmic aspects of adaptive synaptogenesis tailored to edge computing, demonstrate its function using simulations, and design nanomagnetic hardware accelerators for specific functions of synaptogenesis.