Neuromorphic and fully analog in-memory computations are promising for handling vast amounts of data with minimal energy consumption. We have synthesized and studied a series of homo-bimetallic silver purine MOFs (1D and 2D) having direct metal-metal bonding. The N7-derivatized purine ligands are designed to form bi-metallic complexes under ambient conditions, extending to a 1D or 2D metal-organic framework. Owing to the unique structural properties, these complexes exhibit voltage-controlled tunable ionic conductivity, thereby allowing us to demonstrate two-terminal non-volatile memory characteristics with a retention time of more than 104 seconds, an ILRS/IHRS ratio of 107, and volatile memory functionality. The atomistic computations corroborate the dominant influence of the organic framework on controlling ionic diffusion through porous channels. Finally, this capability to tune the ionic conduction in these MOFs was utilized to emulate synaptic plasticity, such as long-term potentiation/depression (LTP/LTD) and complex multi-terminal heterosynaptic plasticity. Attributes of spiking neural networks (SNNs) such as spike time-dependent plasticity (STDP) featuring a unique symmetric anti-Hebbian learning with an impressive STDP ratio of 109, and a paired-pulse facilitation (PPF) index of 60 were recorded, which is among the best for MOF-based neuromorphic devices. Overall, our technique of designing novel metal-organic frameworks with facile porous channels for controlled ionic motion could pave the way for a novel class of materials, allowing seamless integration for bio-synaptic electronic devices.