Sage skill to catch pet ?

[The Legendary Joe]

Does pet have skill in this server or just adding some stat ?

Depends on the pet. Smokie pets let characters with hiding and cloaking to hide from non-boss bugs and demons without being seen.

Isis, Alice, and Sohee all have skills that only activate when both HP and SP are below 50%. Isis casts magnificat when her pet equip is on, Sohee casts heal when she has her accessory on. Alice doesn't have an equip so I believe she needs to be at at least cordial for that.

Most, but not all of the custom pets are looters. Same with the porings. It can be handy on low weight limit characters.Drop your loots and they'll pick em up, make em perform to make them drop their stuffs. The number of inventory spaces they have vary from pet to pet.

And some pets, like Deviruchi (only notable one that comes to mind) do boost stats.