If it's just the antenna line, you'll likely be ahead to cut the old connector off and install a 'standard' connector. Assuming the antenna and feedline are 50 Ohm (typical), a PL-259
is commonly used. If you're using RG-58 coax (typical), you'll also need an RG-58 adapter
for each PL-259. PL-259s fit RG-8 coax natively.
(Note: the PL-258/9 connectors are often called 'UFH' connectors, but really - their performance at even VHF is marginal. Totally unrealistic at UHF freqs. CB is considered 'HF' - they'll work fine for CB, 11m)
Then you can put in a PL-258 barrel connector
and use a standard 'extension' cable. A run of coax with PL-259s on each end.
Uh, I'm assuming the midland rig will accept a PL-259 itself.
gives pretty durn good instructions on how to properly install a PL-259 to various cable sizes (RG-58, RG-8, etc), including how to use the RG-58 adapters.
Or, if you want to avoid the signal loss (measurable, but likely negligible) from an inline connector, run fresh cable from antenna to radio. For max performance, use RG-8 instead of RG-58, but it's tough to route - doesn't bend much or easily. That's why most accept the slight signal loss (special at HF) and use RG-58. The pain of forcing RG-8 into most mobile installs isn't worth it.
Any chance of seeing a picture of this odd-ball connector?
has some better prices on these connectors. No, I've no affiliation with any of 'em.