There isn't one single definitive Gaelic spelling for "Madison." Gaelic (meaning either Scottish Gaelic or Irish Gaelic) doesn't have a direct equivalent name. To create a Gaelic version, you would need to find names with similar meanings or sounds and adapt them.
Therefore, any spelling would be a creative interpretation rather than a true translation. You might consider using elements of Gaelic names that suggest similar qualities (like wisdom, happiness, or strength), depending on the nuance you want to convey.