The phrase "right paw" typically refers to the paw or foot on the right side of an animal's body. It is used to indicate the direction or side that something is being done or performed. Full definition
She limps on front right paw for 5 - 10 seconds after lying down then begins to walk normal. (wagwalking.com)
The cat owners collected «spontaneous» data on whether the cats used their left or right paws when they stepped down the stairs or over objects and whether they slept on the left or right side of their body. (sciencedaily.com)
After investigating all the paws, I found a pretty deep slice in the pad of Spock's back right paw. (tulsapetsmagazine.com)