The Quimby Family is one of the many families who are native to Springfield.
Extended Family Members
Other members include Mayor's dad, Rose Quimby, Clovis Quimby, Freddy Quimby, Agnes Moorehead, Mayor Quimby's niece, Cyrus Quimby, Joshua Quimby, Maria Quimby and Onus Quimby. Mayor's dad got married with Rose Quimby and had two kids, Clovis Quimby and Joe Quimby. But, Mayor's dad has many of children unnamed with his mistress: Agnes Moorehead and all of his son's nannies. Clovis Quimby got married with an unknown woman and had two kids, Freddy Quimby and Mayor Quimby's niece, and Joe Quimby got married with Martha Quimby and had a child, Joey Quimby. But, Joe Quimby has many of children unnamed with his mistress: Miss Springfield and Cookie Kwan. A student named Caroline Quimby was listed on Skinner's list in Yellow Subterfuge.
He may have had an un-named daughter referenced in the comics.
Outside of canon, Joe Quimby alluded to having a cousin named Teddy in the game The Simpsons Road Rage. Teddy was apparently a notoriously terrible driver, as Quimby when dealing with various bad drivers mentioned they were a worse driver than his cousin (note: This is a reference to the real life Chappaquiddick incident where Ted Kennedy infamously had accidentally driven off a bridge with his young colleague, Mary Jo Kopechne, being left to die in the incident by Ted).