Is there a retrograde star that passes closer to the galactic center than our Sun?
There's a whole stream of them: https://iopscience.iop.org/article/10.3847/1538-4357/aadba3
Named Phlegethon, this is a stellar stream that covers about 75⁰ of the sky, and is probably the remnants of a disrupted globular cluster.
It orbits the galaxy retrograde on orbits that take it between 4.9 and 19.8 kpc from the galactic centre. The orbits are highly non-Keplarian. The image shows the orbits with the sun marked as a yellow dot.

Other streams exist and may have similar shaped orbits.