It is forbidden to invite a Non Jew to seudah on Yom Tov, but on Shabbat it is permitted. However, if the Non Jew is an attendant for one of the household members than it permitted to invite him and feed him a well. However, ryo shld not make his food in a separate pan.
Explanation:
The Gemara in Beitzah 21a writes: R’ Yehoshua been Levi said you can invite a Non-Jew on Shabbat but you can’t invite them on Yom Tov. Because oy might make extra food for them…Mareimar and Mar Zutra when a Non-Jew would come by on Yom Tov they would say, “If there is enough for you with what we made then fine otherwise we are not making anything else for you.”
It seems from the Gemara that is forbidden to invite a Non- Jew on Yom Tov but if he shows up, then you are allowed to serve him food from what is already prepared.
The Rambam Hilchot Shvitat Yom Tov 1:2 writes: we do not bake ofr cook on Yom Tov for Non Jews or dogs as the passuk says, “Lachem” prepare for you, not for other nations . Therefore we can invite a Non Jew on Shabbat but onto on Yom Tov because maybe you will cook for him but if shows up then he can eat with them the prepared food.
Why didn’t the Rambam mention the warning that Mar Zutra gave the Non-Jew in the Gemara?
The Taz explains: OH512:4) one could ask what is the purpose of telling the Non jew that we can’t cook have to remind ourselves? So why tell him? So it would seem the Mareimar and Mar Zutra said this to appease him that he wouldn’t get insulted that they are not preparing food for him since it is not alright to cook. There is no actual halacha that comes out of this, so the Rambam left it out.
that Mar Zutra and Mareimar weren’t telling htm that to permit him to sit and eat rather they told him that to calm him down if there wasn’t enough food so he would not get insulted.
It is also seems from the Rambam that it only if the NonJew comes unannounced. The Magen Avraham however brings the Tanya that if the seudah is already prepared then you may even invite a Non-Jew to it. The MA adds that this is only if he decided right then but if they thought about it then no. The Shaar Hatziyun 512:3 quotes the Tanya but rules like the Rambam that only if arrive unannounced. The Tur argues on the Rambam though even if the meal is already prepared rather we and you must warn him.
The Taz bridges the two opinions, (512:4) If the Non-Jew am e by himself her is no concern he put more e food up, but if he pushed him to eat by him since he wants the Non-Jewto come he might make more for him.
The Mishna Berura quotes the machloket between the Rambam and the Tur and he follows the middle opinion of the Taz.
The Rosh (Beitzah 2:13) in Ashkenaz we had the custom of letting the hired help eat with us. R’ Yehoshua ben Levi only forbade inviting a Non-Jew because you like hm and might dd more food in for him.
The Shulchan Aruch 512 says that we are not allowed to cook on Yom Tov therefore you are not allowed, but or your servants or a sudden guest or a Non-Jew who shows up it is pemtted and we are not worried they will make extra.
The Rema writes that one is permitted to make extra for his servants. The Mishna Berura explains the Rema is coming to explains the differs mentioned int e Shulchan Aruch the servandts can have extra food put in the for them since it is one Tircha, one action, But a Non-Jew who comes is only permitted to serve from hat which is ready. Btu not to add.
So it comes out that it permitted to serve the Goy food but only he came by himself, you are allowed to servant household help (so too attendants.) Just you may only add in the pot, not take a new one.