Why, a Shtreimel and Bekishe, of course! That’s the standard “cut and paste”” answer you’ll get for this question. But here’s an answer that might – or might not – surprise you.
“Said the Holy Genius of Sanz, may his merits protect us (this is brought in Chemdah Genuzah), that we have in receiving, that our patriarch Abraham, peace on him, went with (-wore) a Shreimel and a Kaftan, with shoes-and-socks and a Chalat. (Sorry, still no Wikipedia page for the shoes-and-socks one, although you can see a subtle reference to it here. Shoes and socks refers to white stockings and step-in-shoes, traditionally worn by some Chassidim on Shabbos. )
Note the white stockings. This is referred to as “Shich in Zoken” or “Veisse Zoken”
See there [in Chemda Genuzah] that the Seer of Lublin, may his merits protect us, met one Friday a person dressed in the aforementioned attire, and he said to him “Hello”, and that person replied “Gut Shabbos”, and the Seer saw, that that person is not from this world, [so] he asked him “who are you?”, and he answered him “I’m the one to whom God said ‘Go thee out of thy country’“. See there [in Chemdah Genuzah the whole story] at length. But it is appropriate to note herewith, what it says in the book “From Their Mouth and From Their Writings” in the name of Rabbi Yankele of Pshevorsk, may the memory of the righteous be for blessing, on the aforementioned story, that it seems to him that if the Chasam Sofer would’ve seen the patriarch Abraham, he would’ve seen him with a Pressburg hat (I have no idea what this is referring to, do you?), because every sadiq sees the patriarch Abraham according to his level, see there. And this is wonderful.”