Impossible to answer in its current form.

Year 0 didn't exist. So if it has 365 or 366 days, it will mess up the order of days in BC or AD depending which way you're doing the calculation.

If it has 364 days, which is an exact multiple of 7, then it might work, but you'll need to find out what month has one fewer day than normal. Will February have 27 days, or will another month be reduced?

The current calendar has only been in force for the last few hundred years. Projecting back before then is a bit pointless (although I suppose means it could print anything without technically being "incorrect")

Actually this "challenge" is a piece of cake. Simply take a known day (e.g. today, Friday Aug 6), convert that into a number of days (doesn't really matter from when), convert your required day into a number of days, subtract it from the known day and take the remainder after dividing by 7. Subtract the result from the number for Friday (e.g. 6), mod the result by 7 and that gives you the day number, which you can convert back into a day name.

So if you pick a day 3503 days from now, that's 500*7+3, and about 10 years, that's clearly going to be a Monday.