Okay okay, not technically next gen characters since none are offspring of canon characters buuut they are part of my main next gen universe. I wanted to draw something a bit different, so have these.
Mischief (top right): The only pet of Razzleberry Pie, Pinkie and Cheese Sandwich's daughter and eldest child. Mischief is a male 62.5% F1 Savannah Cat (that's 62.5% serval). Mischief is playful and has a lot of energy, often getting into trouble, hence his name. Razzleberry has taught him a variety of tricks and does performances with him.
Phantasm (bottom left): The first pet of Peacherina Darby Pie, Pinkie and Cheese's daughter and third-oldest child (and an older twin). Phantasm is a female Ghost Boa Constrictor. Peach wanted both a reptile and a fluffy mammal as a pet, but her parents would only let her get one at the time. She picked the snake. Phantasm (or Tas) is pretty laidback but also rather clever. She has a strong bond with Peach and is quite protective of both her and her twin brother. She is definitely aware of her ability to be intimidating and will absolutely exploit it in order to freak out anyone bothering her two favourite ponies.
Cookie Dough (also bottom left): Peach's second pet. Peach acquired him several years after Phantasm as a small shaggy pup. He proceeded to grow into a very large, very enthusiastic, uber-fluffy Saint Berdoodle dog. Cookie Dough (also known as Dough, Doughy, and Dough Head) is not the sharpest knife in the drawer but he certainly tries. He loves everybody in the family, other pets included, and is generally just friendly to everything. Peach grooms him herself, having gotten plenty of practice in dealing with fluff thanks to her and her twin brother's genetic fluke of having extra-fluffy coats.
Morsel (bottom right): The only pet of Fluffernutter Sandwich, Pinkie and Cheese's son and youngest child (and Peach's younger twin). Peanut got Morsel on the same day as Peach got Phantasm- the twins requested getting their own pets for their 12th birthday. Their parents obliged and brought them to Fluttershy's first, where they both managed to find something they liked. Morsel (or Mo) is a male Asian Water Monitor. Though large (and very carnivorous), Morsel is a big sweetheart. Being raised by a kind doofus like Peanut probably had something to do with that. Having Gummy around likely helped too. A lot of ponies have been startled when Peanut introduced them to Morsel- most don't expect somepony like him to own a huge meat-eating lizard. (Morsel is larger than Cookie Dough, it doesn't show well here. I think I drew Morsel smaller to emphasize how big Gummy is)
Gummy (also bottom right): Pinkie Pie's beloved pet alligator. The bright green reptile underwent a massive growth spurt around his 3rd birthday and never quite stopped. His teeth finally started coming in too. His growth did dial back after some years, but the alligator is still continuing to slowly grow larger. At Gummy's current point, where his growth is steadying out and is much slower now, he's still sitting at nearly 20 feet in length and approaching 2,000 pounds at just 15 years old. Twilight's tried researching alligators to find an explanation for such dramatic growth and massive size, but came up empty. The present theory is Gummy either a) Has a freak but natural genetic mutation that isn't suppressing his growth to normal levels, b) His genetic code has somehow become mutated due to exposure to powerful magic (namely the Elements of Harmony and Discord's chaos powers), or c) He's not 100% alligator and has some other reptilian creature in his genes that is causing his size.