1st hour, 2nd hour, 3rd hour... But how to say "zero"-th hour?

E.g. in School we have 5-7 or 8 hours every day (Math, History, Biology, Chemistry, English etc.).

The first hour starts at 8:00 A.M.

But every Thursday we have an hour that stars at 7:10 A.M.

In the table it will look like this (just random picture from the web):

In Czech language we call it:

nultá hodina which is something like zero-ish hour

and then 1st, 2nd and 3rd: první, druhá, třetí hodina

How is nultá hodina (the hour that is before the first hour) called in English?

And how do you write it "shortly"? As 0th ? Or somehow else?

You already had the answer: it’s zeroth.

I think you’ll find that -th is a modestly productive suffix in English for indicating ordinals other than first, second, and third. For example, consider the n^th element in a series, or the i ^th and j ^th indices of (two-dimensional) matrix. You can even find “epsilonth” (ε^th) if you look hard enough.

But that one’s rare; zeroth is not. The OED defines zeroth as:

Coming next in a series before the one conventionally regarded as the first.

Its first citation is from the 19^th century. So the two series work out to be:

• In words: zeroth, first, second, third, fourth, fifth, . . . three hundred ninety-fifth, . . .

• In figures: 0^th, 1^st, 2^nd, 3^rd, 4^th, 5^th, . . . 395^th, . . .

In English, most people would not recognize the term 'zeroth'. Ordinal numbers start at 'first'. Any other starting point is either a neologism or jocular.

For the hour -before- the first hour, well, that just means what you're calling the first hour is mislabeled and should instead be labeled the second hour.

The case you gave is interesting, where it is an exception to the schedule for one day to have an additional hour before the hour labeled 'first'. To call it 'zeroth' hour would be strange (perfectly recognizable and used by any math geek, but there it is). But then what is the hour that comes before that? There is no word for it that is generally recognizable in English so some other locution would be used, like 'early morning hour' or 'special early class' or something relevant to its function.

Consider this century. In English, it is referred to as the twenty-first century, even though it starts with 20. That's because if you count backwards to the start of the Christian time labeling, the first years marking from when Jesus Christ was supposed to be born is called the 'first century' but isn't the years 101-200 but rather 1 through 100. Czech may do it differently, but this is how it is done in English.