IIRC
35 Remington was a rimless cartridge in a series 25, 30, 32, and 35 Remington, meant to compete with the Winchester 25-35, 30-30, and 32 Special lever gun ctgs. The only survivor of the Remington line is the 35, which you have. You should be able to pick up the ammo anywhere 30-30 is sold as Marlin still chambers rifles for it and it is a popular deer hunting cartridge. HTH