Grandma Barksdale
The mother of Helen Morgendorffer, Rita Barksdale, and Amy Barksdale, who is never directly seen or heard from in the Daria series. Her presence, however, is felt from Erin's wedding onward ("I Don't"). An old lady who could be Grandma Barksdale is shown with a (bored) baby Daria in "The Daria Diaries".
It is implied in "I Don't" that she's unable to travel at that time, and also implied that she is well off enough financially to afford showering Rita and her daughter Erin with gifts and windfalls. (Glenn Eichler has said Helen didn't grow up in a wealthy household, but the show itself does show Barksdale with money) We know she could help fund college funds for Daria and Quinn, but doesn't. "Diaries" has Helen making a note to talk with Rita and Amy about who gets Grandma Barksdale for the holidays. "The Daria Database" has Daria refer to a visiting grandmother as being incontinent - and since Ruth Morgendorffer doesn't seem to be, then it has to be Grandma Barksdale. If so, she visited the Morgendorffers at Lawndale around Season 2.
Of her three daughters, she is closest to Rita and appears to favor her over Helen and Amy. This spawned a long-running feud between the three sisters that is finally (one hopes) resolved in "Aunt Nauseam." Before then, Helen occasionally rants about the unfair treatment Rita and Erin get, said rants being remarkably similar to her husband Jake Morgendorffer's rants against his father.. Rita once attacked Helen and Amy for never calling their mother themselves, and said that they were partially to blame for the bad relationship; Amy gave a bitter response (with Helen's agreement) of "Why should we when she's never offered us the slightest bit of encouragement or appreciation?".
In fanon, it's assumed she paid for Brian Danielson to fly out to Switzerland to have a second honeymoon with Erin, saving their marriage ("Aunt Nauseum"): Brian didn't have a job to pay for it on his own, and she'd already sent Erin there.
Fanfiction
The character was expanded in numerous fanfics, with many divergent names.
C.E. Forman gave her an equally wealthy half-sister, Aunt Eleanor, and the same rivalry that Helen/Rita had with Amy and Quinn with Daria. Kara Wild named her Evelyn in the Driven Wild Universe and made her generally crusty, but loving. Later, Richard Lobinske would create Tess Barksdale, the southern matriarch in the fanfiction series, Falling Into College. Roentgen introduced a Bethany Barksdale for The Hallowed Halls of Fielding, a connected upper-class matriach, paying for Quinn & Daria's Fielding Prep education and ignoring Helen's authority in her attempts to mould Quinn into a 'proper' high society lady. The "punkverse" shared world has Edie Barksdale, a moderately wealthy woman from a 'good' family: Brian Taylor's 1980s-set Moving Pictures has badly coping after the death of her husband and having a disintegrating relationship with Amy and Helen; in Charles RB's "God Save The Esteem", she was cut off from seeing Daria early on and in the 00s, is trying to revive their relationship in an attempt to 'retrieve' the girl.