Many efforts have been made to improve the neuron integration efficiency on neuromorphic chips, such as using emerging memory devices and shrinking CMOS technology nodes. However, in the fully connected (FC) neuromorphic core, increasing the number of neurons will lead to a square increase in synapse & dendrite costs and a high-slope linear increase in soma costs, resulting in an explosive growth of core hardware costs. We propose a co-designed neuromorphic core (SRCcore) based on the quantized spiking neural network (SNN) technology and compact chip design methodology. The cost of the neuron/synapse module in SRCcore weakly depends on the neuron number, which effectively relieves the growth pressure of the core area caused by increasing the neuron number. In the proposed BICS chip based on SRCcore, although the neuron/synapse module implements 1∼16 times of neurons and 1∼66 times of synapses, it only costs an area of 1.79 × 107 F2, which is 7.9%∼38.6% of that in previous works. Based on the weight quantization strategy matched with SRCcore, quantized SNNs achieve 0.05%∼2.19% higher accuracy than previous works, thus supporting the design and application of SRCcore. Finally, a cross-modeling application is demonstrated based on the chip. We hope this work will accelerate the development of cortical-scale neuromorphic systems.