Recently, unmanned aerial vehicles (UAVs) are deployed in Novel Coronavirus Disease-2019 (COVID-19) vaccine distribution process. To address issues of fake vaccine distribution, real-time massive UAV monitoring and control at nodal centers (NCs), the authors propose SanJeeVni, a blockchain (BC)-assisted UAV vaccine distribution at the backdrop of sixth-generation (6G) enhanced ultra-reliable low latency communication (6G-eRLLC) communication. The scheme considers user registration, vaccine request, and distribution through a public Solana BC setup, which assures a scalable transaction rate. Based on vaccine requests at production setups, UAV swarms are triggered with vaccine delivery to NCs. An intelligent edge offloading scheme is proposed to support UAV coordinates and routing path setups. The scheme is compared against fifth-generation (5G) uRLLC communication. In the simulation, we achieve and 86% improvement in service latency, 12.2% energy reduction of UAV with 76.25% more UAV coverage in 6G-eRLLC, and a significant improvement of ≈199.76% in storage cost against the Ethereum network, which indicates the scheme efficacy in practical setups.