Who makes 35 caliber rifle ammo?

Depends on WHICH .35 caliber- there are several different cartridges that fall into that category. Winchester, Remington, Federal and Hornady all have some .35 rifle loads. But you will need to check with a REAL gun store or on-line. Do not expect the chain stores with a gun section to carry it. The current month's issue of American Rifleman has a good article on a half dozen different .35 caliber rifles.