Noticed there wasn't a set of rules for Medium Cats as Animal Companions. I Created one that I think fits well between the two types. It doesn't have the penalty of large size or the benefits of a small size, and the stats are in the middle of the two. Here's what I came up with:
Starting Statistics: Size Medium; Speed 40 ft.; AC +1 natural armor; Attack bite (1d6), 2 claws (1d3); Ability Scores Str 12, Dex 19, Con 13, Int 2, Wis 14, Cha 8; Special Attacks rake (1d3); Special Qualities low-light vision, scent.
7th-Level Advancement: Size Medium; AC +2 natural armor; Attack bite (1d6 plus trip) , 2 claws (1d4); Ability Scores Str +4, Dex 0, Con +2; Special Attacks: grab, pounce, rake (1d4).
Go to Pathfinder Druid Animal Companion Rules.
Alternatively you could swap out one of the Special Attacks for Sprint, but keep in mind that specifically works best for a Cheetah. No other real world cat has that type of speed.
Comments about cat species:
A Puma, Cougar and Mountain Lion are actually all the same animal. Because they can also have a black variation, they are sometimes Panthers.
https://animalfactguide.com/animal-facts/cougar/
Technically a Panther is not a species of cat. Usually we think of the black variation of a Leopard (A Small Cat) but because they can actually be from any species you could have a black cougar; hence why I listed them.
https://nerdist.com/black-panthers-are-not-a-species-so-what-are-they/