Nećak se jutros držao za mamu kad je došao u vrtić.

Because the subject is nećak (nephew), which is a masculine singular noun.

In the Croatian past tense, the -l participle agrees with the subject in gender and number:

• držao = masculine singular
• držala = feminine singular
• držalo = neuter singular
• držali = masculine personal plural, etc.

The same is true for došao: it also matches nećak.

Here se is part of the verb expression držati se za + accusative, which means to hold on to, to cling to, or to grab onto someone/something.

So:

• držati = to hold, keep
• držati se = to hold on, cling
• držati se za mamu = to hold on to mom

Without se, the meaning changes.

This is a very common learner question.

In the first clause, the verb is reflexive-like with se: držao se. In this kind of 3rd person singular past form, Croatian normally says:

• On se držao not On se je držao

So the sentence is completely normal as written.

In the second clause, the verb is not using se, so you get the regular past form:

• kad je došao

A useful comparison:

• Držao sam se za mamu. = I held on to mom.
• Nećak se držao za mamu. = The nephew held on to mom.

Yes, za can mean for, but not here.

After držati se, the pattern držati se za + accusative means to hold onto someone/something physically.

So in this sentence:

• za mamu = onto mom / to mom in the sense of clinging to her

It does not mean for mom here.

Because za in this expression takes the accusative, and mama changes in the accusative singular to mamu.

So:

• nominative: mama
• accusative: mamu

This is very typical for feminine nouns ending in -a.

Jutros means this morning.

It is a time adverb, so it does not change form for case, gender, or number.

Examples:

• Jutros pada kiša. = It’s raining this morning / It rained this morning, depending on context.
• Jutros sam radio. = I worked this morning.

In your sentence, it tells you when the action happened.

Yes. Croatian word order is fairly flexible.

Your sentence has a natural order:

• Nećak se jutros držao za mamu...

But you could also hear:

• Jutros se nećak držao za mamu...

The difference is mostly about emphasis or style. Putting jutros first gives it a bit more focus.

Because se is a clitic. Croatian clitics usually appear very early in the sentence, often in the second position.

So se tends to come right after the first stressed word or phrase:

• Nećak se jutros držao...

This sounds much more natural than placing se later.

The same general rule applies to other clitics like je, sam, ga, mu, and so on.

Both kad and kada mean when.

• kad = shorter, very common in everyday speech
• kada = a bit fuller, sometimes more formal or careful in tone

So here kad je došao u vrtić is completely normal and natural.

Because this sentence expresses movement toward a destination.

Croatian uses:

• u + accusative for motion into / to
• u + locative for location in

So:

• došao je u vrtić = he came to kindergarten
• bio je u vrtiću = he was in kindergarten

Here the child is arriving there, so u vrtić is correct.

The subject is still nećak.

So the sentence means that the nephew was holding onto his mom when he came to kindergarten.

The masculine singular form došao shows that it refers back to nećak.

If it referred to mama, it would need to be feminine:

• kad je došla u vrtić

You could, but the meaning would change.

• držao je mamu = he was holding mom
  This is more direct and does not automatically imply clinging to her.

• držao se za mamu = he was holding onto mom / clinging to mom
  This is the best choice for a shy or upset child at the kindergarten entrance.

• držao se mame can sound different, more like stayed close to mom, stuck with mom, or in some contexts relied on mom. It is not the clearest way to express the physical image in this sentence.

So držao se za mamu is the most natural phrasing here.