Kasirka kaže da danas nema popusta na ove patike.

Kasirka means female cashier. Serbian often marks the gender of a person in job titles:

• kasir = male cashier
• kasirka = female cashier

So this sentence is specifically talking about a woman.

Kaže is 3rd person singular present tense: he/she says.

So:

• ja kažem = I say
• ti kažeš = you say
• on/ona kaže = he/she says

Here, kasirka kaže = the cashier says.

Here da means that and introduces a subordinate clause:

• Kasirka kaže da... = The cashier says that...

This is very common after verbs like:

• kaže = says
• misli = thinks
• zna = knows
• veruje = believes

Serbian often does not use a separate dummy subject like English there.

So instead of literally saying there is no discount, Serbian says:

• nema popusta = there is no discount

Here nema does the job of expressing non-existence or absence.

Because after nema, Serbian very often uses the genitive when talking about absence.

• popust = nominative singular
• popusta = genitive singular

So:

• ima popust is not the normal pattern here
• nema popusta = there is no discount

This is a very common structure:

• nema vremena = there is no time
• nema novca = there is no money
• nema problema = there is no problem / no problems

They mean different things.

• nema = there is no / there are no / does not have
• nije = is not

So:

• nema popusta = there is no discount
• nije popust = it is not a discount

In this sentence, the idea is that the discount does not exist today, so nema is the correct choice.

Because popust normally goes with na + accusative when you say what item the discount applies to.

Examples:

• popust na patike = discount on sneakers
• popust na knjige = discount on books
• popust na jakne = discount on jackets

So na ove patike is the normal Serbian pattern.

It is accusative plural.

That is because na after popust takes the accusative here.

For feminine plural inanimate nouns, the nominative and accusative often look the same:

• nominative: ove patike
• accusative: ove patike

So even though the form looks unchanged, the case is still accusative because of the structure popust na + accusative.

Because patike is a feminine plural noun, and the demonstrative must agree with it.

Compare:

• ovaj = this, masculine singular
• ova = this, feminine singular
• ovo = this, neuter singular
• ove = these, feminine plural

Since patike is feminine plural, ove is the correct form.

Patike usually means sneakers, trainers, or athletic shoes in everyday Serbian.

The singular is patika, but in real life people very often use the plural because shoes normally come as a pair:

• patika = one sneaker
• patike = sneakers / a pair of sneakers

Yes. Serbian word order is fairly flexible.

The given sentence is neutral and natural:

• Kasirka kaže da danas nema popusta na ove patike.

But other orders are also possible, depending on emphasis:

• Kasirka kaže da nema popusta danas na ove patike.
• Danas kasirka kaže da nema popusta na ove patike.

The original version sounds like a normal, straightforward statement.

A helpful approximation is KAH-zheh.

The important sound is ž, which sounds like the s in measure or the g in beige.

So:

• ž = a soft buzzing zh sound
• kaže ≈ KAH-zheh

Not exact English, but close enough to get started.