Çocuğu yanağından öptü.

Because çocuğu is the definite/specific direct object form.

• çocuk = child
• çocuğu = the child / that child as the object of the verb

Turkish often marks a specific direct object with the accusative ending -(y)ı / -(y)i / -(y)u / -(y)ü.

Here:

• çocuk
  • -u → çocuğu

The stem changes slightly because final k often softens to ğ before a vowel-initial suffix.

So the sentence is using çocuğu because the person kissed a specific child, not just a child in a general sense.

Yes, in isolation it can be ambiguous.

It can be:

• çocuk + -u = the child (accusative)
• çocuk + -(s)ı = his/her child

But in this sentence, the normal reading is the child as the direct object.

If you clearly wanted his/her child as a specific direct object, standard Turkish would usually use çocuğunu:

• çocuğunu öptü = he/she kissed his/her child

So in Çocuğu yanağından öptü, learners should normally understand çocuğu as the child.

It breaks down like this:

• yanak = cheek
• yanağı = his/her cheek
• yanağından = from his/her cheek

More mechanically:

• yanak
• -ı = 3rd person possessive
• -n- = buffer consonant
• -dan = ablative ending, often meaning from

So yanağından literally looks like from his/her cheek, even though the natural English meaning here is on the cheek.

This is a normal Turkish pattern with some body-part expressions.

With verbs like öpmek (to kiss), Turkish often uses the ablative on the body part to show the part affected:

• yanağından öpmek = to kiss on the cheek
• alnından öpmek = to kiss on the forehead
• elinden tutmak = to hold by the hand

So even though -dan/-den often means from, in this kind of expression it works more like on/by the ... in English.

Normally, it refers to the child's cheek.

So the natural interpretation is:

• He/she kissed the child on the cheek

Turkish often uses a possessed body-part noun like this without repeating the owner explicitly. In context, the owner is usually understood to be the person affected by the action.

Here, that person is çocuğu.

Because Turkish often changes final k to ğ when a vowel-initial suffix is added.

So:

• yanak → yanağı
• çocuk → çocuğu

This is a very common sound change in Turkish.

Other examples:

• kulak → kulağı
• ayak → ayağı

Also, ğ in modern Turkish is usually very soft; it often just lengthens or smooths the previous vowel rather than sounding like a strong consonant.

That n is a buffer consonant.

After the 3rd person possessive suffix, Turkish often inserts -n- before another suffix, especially a case ending.

So:

• yanağı = his/her cheek
• yanağı + dan becomes yanağından

That n helps the word flow and is part of normal Turkish morphology.

Because the past tense ending changes according to consonant harmony and vowel harmony.

The past tense suffix is usually written as -DI, but its real form changes:

• after a voiceless consonant like p, it becomes -TI
• the vowel changes by vowel harmony, so here it becomes -tü

So:

• öp-
  • -DI → öptü

That means kissed.

Turkish often omits the subject pronoun if it is already understood.

So öptü by itself can mean:

• he kissed
• she kissed

Turkish does not mark gender in the verb here, so the sentence does not tell you whether the subject is male or female.

A full version could be:

• O çocuğu yanağından öptü. = He/She kissed the child on the cheek.

But the o is often left out.

Because Turkish normally puts the verb at the end.

A very common basic pattern is:

• Subject + Object + other information + Verb

So here, roughly:

• (O) = subject, omitted
• çocuğu = direct object
• yanağından = body-part phrase
• öptü = verb

This is a very natural Turkish order.

Other word orders are possible for emphasis, but this one is straightforward and standard.

That is an important difference.

• Çocuğu yanağından öptü
  The direct object is the child.
  The body-part phrase tells you where the child was kissed.
  → He/she kissed the child on the cheek.

• Çocuğun yanağını öptü
  The direct object is the child's cheek.
  → He/she kissed the child's cheek.

In English, these can sound very similar, but Turkish structures them differently.

So your sentence focuses on the child as the object, while Çocuğun yanağını öptü focuses on the cheek as the object.