Board Thread:Questions and Answers/@comment-31826204-20170424185554/@comment-27701762-20170424201134

There is no clear definitive answer. There are quite a few people who think that Gaster is related to Sans and Papyrus in some way, usually as a father to the two, but the only evidence for such a position is that the "W.D" may (and to be fair, likely) refers to "WingDings," making a connection via the use of fonts as names. But another theory, which fits just as well, is that Sans and Papyrus are fragments of Gaster left behind when he fell into his experiment.

There's not really any way to specifically say that any given theory is right or wrong. We could point to the fact that Sans and Papyrus never mention having a lost brother, nor does anyone else mention a lost brother, but the same is true of Sans and Papyrus never mentioning having a father.