Ola tudo bem?
Esta correto falar assim?
I will have to pay you on day 4.
I will have to pay you on January 4th.
Your question suggests (even if slightly) that you will prospectively ask whether you can pay in another month, so it would be pointless to state just the day. My thinking here, obviously.
Anyway, I will answer your question just the same.
If you want to pay in this month (the current month):
Let´s imagine today is September, 1; then you would just ask "when do I have to pay? Could be on April 4th?
To the following month, we could ask "could I pay on the next 04th of May? (insert the month you wish to)".
There are other ways to ask that, with "shall" for example (but I think it is less colloquial, more formal in kind). Let´s wait for more comments.