What is the fastest ocean deep current?
This article in Fox News points to this paper and asserts that the fastest deep current measured is the Antarctic.

Rintoul, of the Antarctic Climate and Ecosystems Cooperative Research
Center in Hobart, said it proved to be the fastest deep ocean current
yet found, with an average speed of 7.9 inches a second (0.20 m/s).

I have no access to the paper, I can only read the abstract. I guess Fox News didn't lie this time as they are sourcing a scientifical paper of Nature Geoscience.
Fukamachi, Y., Rintoul, S., Church, J. et al. Strong export of Antarctic Bottom Water east of the Kerguelen plateau. Nature Geosci 3, 327–331 (2010). https://doi.org/10.1038/ngeo842