15" tires won't fit on a 16" rim.
I run 235/75-15 Duratracs on Ravine rims that came as an option for TJ's. They clear the calipers.
OTOH, Canyon rims won't due to the way the spokes curve back toward the calipers
Take a look at these threads for more info:
Patriot wheels sizing
15" Wheels and 30" tires on your Patriot (no spacers): Test Fit Results