We present an on-chip trainable neuron circuit. Our proposed circuit suits bio-inspired spike-based time-dependent data computation for training spiking neural networks (SNN). The thresholds of neurons can be increased or decreased depending on the desired application-specific spike generation rate. This mechanism provides us with a flexible design and scalable circuit structure. We demonstrate the trainable neuron structure under different operating scenarios. The circuits are designed and optimized for the MIT LL SFQ5ee fabrication process. Margin values for all parameters are above 25\% with a 3GHz throughput for a 16-input neuron.