Central and peripheral biological clocks are essential to regulate creatures’ circadian rhythms, mimicking the biological clock controlled neural and/or immunological responses are research hotspots in the emerging neuromorphic or brain-like systems. However, the current neuromorphic devices still depend on programmable frequency dividing and doubling machine clocks, the high system cost is a challenge to conduct sophisticated brain-like neuromorphic computing. Herein, a dual biological-clocks (including ambient light and endocrine) controllable fibrous synapse crossbar array is proposed. It is demonstrated and confirmed in this work, the Ag conductive filaments, which are critical in the conventional MXene synapses, can be successfully switched by differently biased MoS2/MXene heterojunction. The current and power of the unit fibrous synapse in positive/negative switching processes can reach as low as 460 pA/-170 pA and 330 pW/121 pW, respectively. Then, four kinds of logical calculations to the input light signals are accomplished by using the as-prepared fibrous synapse based logical gate. Meanwhile, the light and serotonin combined modulation on the synaptic currents are manifested and applied to simulate the immune-neural responses (memory and the memory exhausted) of T cells in the skin clock. More interestingly, two biological immune compensation mechanisms controlled by the central clock and peripheral clock, namely balanced and reset immune compensation, are also accomplished. This work may pave a new way for promoting the development of dual biological-clock regulated computations in neuromorphic systems.