Future connected and autonomous vehicles (CAVs) will operate at different autonomous levels for decades. Therefore, we propose a novel prioritisation scheme according to the autonomous levels of CAVs, and a corresponding multiple access mechanism, to be named full-duplex prioritised scheduling (FDPS) protocol, to enhance the delivery of high-priority packets in future New Radio (NR) enhanced vehicle-to-everything communication (eV2X) vehicular ad hoc networks (VANETs). Comparing to the standardised sensing-based semi-persistent scheduling (SB-SPS) protocol, this paper presents how collision detection is enabled during the broadcast, how collisions are resolved, how the priority of a packet from a colliding CAV is recognised, and how the broadcast of high-priority packets is enhanced. Both protocols are evaluated through mathematical formulations and simulations in terms of average successful packet delivery rate (PDR), collision duration, and latency. Simulation results have firstly validated the mathematical analysis, they have also shown the enhancement of packets delivery in future NR eV2X VANETs when the self-interference suppression (SIS) factor is better than 16%, which is achievable by deploying the existing SIS technologies.