Game Of Thrones: 7 Fan Theories About Jon Snow 's Parents (That Aren't R+L=J)
2. B+A=J, R+L=D
The main part of this theory is the first, that the father of Jon is Brandon Stark (Ned's older brother), and his mother is Ashara Dayne (sister of Ser Arthur). The secondary part is that Rhaegar and Lyanna did indeed have a child, but it was actually Daenerys.
Ashara Dayne is a popular choice for being Jon's mother, the most commonly thought of after Lyanna, and there are reports that point to her having had a child, or at least being pregnant. She was with both Brandon and Eddard Stark at the Tourney of Harrenhal, and Ser Barristan Selmy claims that one of them bedded her afterwards. She later committed suicide, and was believed to be pregnant at that time. Having Brandon as the father fits with Ned not being Jon's dad, but still possessing Stark blood, although given he died around a year before Jon's birth, it would mean that they have been lying about Jon's age (which, of course, isn't totally impossible, as they may lie about it in order to avoid conflict over an older bastard and younger legitimate child).
The R+L=D element of this is slightly trickier, since Daenerys' birth at Dragonstone during the storm has already been discussed, and there isn't a great deal to go on, even if it would make for a rather big plot twist and allows for other theories while still having something come of Rhaegar and Lyanna.