Nakon sat vremena na ekranu se pojavi moj redni broj.

Nakon requires the genitive case, so you need a genitive form after it.
The phrase sat vremena is a very common fixed expression meaning an hour (of time), literally an hour of time, where vremena is genitive singular of vrijeme.

You’ll also hear:

• nakon jednog sata = after one hour (more explicit, also genitive)
• nakon sat vremena = after an hour (very common, natural)

In nakon sat vremena, the whole time expression functions as genitive (because of nakon).

Inside the phrase:

• sat is effectively the head noun meaning hour
• vremena is genitive of vrijeme, used like of time

So structurally it’s like: (after) [an hour] [of time].

Because na can take different cases depending on meaning:

• na + locative = location (where?): na ekranu = on the screen
• na + accusative = motion/goal (to where?): na ekran = onto the screen

Here you’re describing where the number appears (location), so na ekranu is correct.

Ekranu is locative singular of ekran.
It’s used because of na with the meaning on (a location).

Base form (dictionary): ekran
Locative singular: na ekranu

This is the verb pojaviti se = to appear.
The se is part of the verb (a reflexive clitic). It does not mean himself/itself in the literal English reflexive way; it’s just how Croatian forms this verb.

So:

• pojavi alone isn’t the same meaning
• pojavi se = appears / shows up

In a normal main clause, se is a clitic and usually goes in the second position of the sentence/clause.

Here the order is: Nakon sat vremena | na ekranu | se | pojavi | moj redni broj.

You can also say na ekranu pojavi se moj redni broj, but it sounds more marked/less neutral. The given order is very natural.

Pojavi is present tense (3rd person singular) of the perfective verb pojaviti se.

With perfective verbs, the present form is very often used with future meaning, especially when the time is clearly set:

• Nakon sat vremena ... se pojavi ... = After an hour, it appears / will appear.

Depending on context, it can also be used as a vivid “storytelling present” in narration, but the form itself is present.

Pojaviti se is perfective: it focuses on the event as a single completed “appearance” (the moment it shows up).
The imperfective partner is commonly pojavljivati se: it focuses on repeated or ongoing appearing.

Examples:

• Broj se pojavi. = The number appears (once, as a completed event).
• Broj se pojavljivao. = The number kept appearing / was appearing repeatedly.

Because moj redni broj is the subject of the verb se pojavi (it is the thing that appears).

So it’s nominative:

• moj (my) = nominative masculine singular
• redni (ordinal) = nominative masculine singular
• broj (number) = nominative masculine singular

All three agree in gender, number, and case.

Redni broj literally means ordinal number / sequence number: the number that indicates your position in a list/queue/order.

Croatian uses this collocation very often in contexts like:

• waiting systems (ticket number)
• lists, rankings, numbered entries

Just broj is more general (number). Redni broj specifies that it’s your number in order.

Croatian word order is flexible, but not random. The sentence is arranged in a very natural “scene-setting” way:

1) time: Nakon sat vremena
2) place: na ekranu
3) clitic: se
4) verb: pojavi
5) subject/new info: moj redni broj

You can rearrange parts for emphasis, but you must still respect clitic placement rules and case endings.

A common past-tense version would use the past tense (perfect):

• Nakon sat vremena na ekranu se pojavio moj redni broj. (masc. subject broj)
• If the subject were feminine, the past form would change accordingly.

The given sentence can sound like instructions (“what happens next”) or a vivid description, while the past version is straightforward storytelling.