The computational complexity of deep learning algorithms has given rise to significant speed and memory challenges for the execution hardware. In energy-limited portable devices, highly efficient processing platforms are indispensable for reproducing the prowess afforded by much bulkier processing platforms. In this work, we present a low-power Leaky Integrate-and-Fire (LIF) neuron design fabricated in TSMC's 28 nm CMOS technology as proof of concept to build an energy-efficient mixed-signal Neuromorphic System-on-Chip (NeuroSoC). The fabricated neuron consumes 1.61 fJ/spike and occupies an active area of 34 $μm^{2}$, leading to a maximum spiking frequency of 300 kHz at 250 mV power supply. These performances are used in a software model to emulate the dynamics of a Spiking Neural Network (SNN). Employing supervised backpropagation and a surrogate gradient technique, the resulting accuracy on the MNIST dataset, using 4-bit post-training quantization stands at 82.5\%. The approach underscores the potential of such ASIC implementation of quantized SNNs to deliver high-performance, energy-efficient solutions to various embedded machine-learning applications.