Take a today's molten salt reactor with added automatic chemical extraction of fission products and dumping it overboard and couple it with ionic thrusters at 1

Take a today's molten salt reactor with added automatic chemical extraction of fission products and dumping it overboard and couple it with ionic thrusters at 100x voltage of the ones already working at NASA, and you can get to 0.01c in few years. 2-4 stages and get to Alpha Centauri in 100-200 years. And we're talking about ship of at least several tons reaching the destination, not just small chip.