Max first appeared in the animated series Goof Troop as an 11 year old boy who's the only son of Goofy. It's unknown who the mother is as she died when Maxie was fairly young and has never been revealed or name mentioned. Over the years since he was created in 1992 he's been aging making him one of the few Disney characters that actually ages. Ironically despite the hate relationship with Pete and Goofy Max happens to be best friends with Pete's son PJ who happens to live next door to Max.
Max hits the big screen in A Goofy Movie where he's a 14 year old highschooler trying to impress a girl named Roxanne who he likes by telling her that he'll appear on screen with a band called Powerline during one of their concerts. Though this doesn't exactly work out smoothly as Goofy takes Max on a father and son road trip that causes some bumps in the road. Strangely in the next movie Max appears in Mickey's Once Upon A Christmas Max is very young so it can be safe to assume this takes place around the Goof Trip timeline. Due to the popularity of A Goofy Movie a sequel was made where Max is 18 and heading into college. This is the last movie Max has appeared in but he has appeared in the show The House Of Mouse after this.
A Goofy Movie
Once Upon A Christmas
The House Of Mouse
An Extremely Goofy Movie
Mickey's Twice Upon A Christmas