This is the fourth, and currently final entry of Redeeming Little Miss Mary Sue
One of the things that will almost always raise a cry of “Mary Sue!” is creating a blood relative of an established character, particularly a twin of the opposite sex. For fledgling writers, there’s an understandable allure to making one’s character a sibling of an established character. After all, siblings share a lot of genes and experiences, so it would make sense that if Sonic the Hedgehog had a twin sister that she’d share his super speed and other talents, right? While you could make a valid argument for that, such an argument requires a lot more work than an inexperienced author is likely to put into their writing. Simply inserting a sibling, or even a cousin, where none existed before and expecting the audience to accept it as easily as the other characters in your story is going to make people accuse you of lazy writing at the least, if not of you creating a Mary Sue. Creating new family members for characters long after a story has started and gained a following can cause backlash for original fiction as well as fanfics. It must be handled with care and perhaps a bit of lampshade hanging to convince the readers to play along.
Creating romantic relationships between a canon character and your original creation can raise red flags as well, depending on the audience. Romance and love is a core genre of the fanfiction community, as many people enjoy imagining their favorite characters hooking up. Romantic pairings, or “ships” in the common fandom dialect, are also frequently a point of contention between fans, although only the most rabid shippers will attack ships incompatible with their own on principle. Pick any two canon characters from a piece of work, and you’ll probably be able to find an audience for a fic centered around them. Canon characters shipped with original characters, however, will have a harder time finding acceptance because the original character will be an unknown quantity to your readers. I don’t write romance-centric stories myself, but I’m pretty sure this general piece of advice is applicable: take the time to let your readers get to know and like your original character before doing something huge with them - including getting them in a serious relationship.
That said, feel free to start your character off with having a crush on a main character. That’s a trait that serve as a seed for character development, fun scenes, and possible reciprocation of those feelings later on.
One aspect commonly misused by Mary Sue characters that could actually redeem them is their personal history and relationship to the history of the canon universe. For Little Miss Mary Sue, history is just part of the character trait checklist I’ve warned against before: a mostly cool-sounding but pointless lists of accomplishments and tragedies with no bearing on Mary’s current character or any logical relationship to the world she inhabits. My own Traev character provides a nice extreme example of misused history: when I first conceived him, his backstory was basically a more coherent version of my imaginary childhood adventures through my favorite books, movies, and video games. Traev had traveled to and been influential in places such as Genesis-era Sonic the Hedgehog, Harry Potter, Pokemon, Digimon Adventure & 02, Animorphs, and probably much more - although the series I’ve listed all were significant influences on Traev’s abilities. None of those were of any importance to the story I was attempting to craft around Traev and his three hangers-on, and when I figured that out I wiped Traev’s history and made a new one that actually had importance to the story.
Making your original character’s history fit the world he or she inhabits will go a long way toward both making them appear more palatable to readers and giving the character depth and opportunities for development. You don’t always have to make the character fit the world; it is perfectly ok to alter the world’s history to fit your character (such as if you really want to make a twin sister for one of the Saiyans in Dragon Ball Z) so long as you put in the effort to make the changes appear reasonable to the reader. Alternate Universes, where the world is significantly different from the canon due to one or more big changes in history, are another fanfiction mainstay. When inserting a character into a universe with the intention of claiming “they were always there,” take consideration for how the newcomer’s presence will affect every other character’s attitude and choices prior to the start of your story as well as during it. Addressing such things will make your writing appear less lazy and the character less like a Mary Sue.