Trafik işareti parkmetrenin yanında.

In Turkish, a present-tense to be is often omitted in simple third-person sentences.

So:

Trafik işareti parkmetrenin yanında.
literally looks like
Traffic sign parking meter's side-at.

But it naturally means:

The traffic sign is next to the parking meter.

This is very normal in Turkish. If you wanted a different tense, you would show it more clearly:

• Trafik işareti parkmetrenin yanındaydı. = The traffic sign was next to the parking meter.

Because trafik işareti is a common Turkish noun-compound pattern.

In Turkish, when one noun modifies another noun, the second noun usually takes a special ending. So:

• trafik = traffic
• işaret = sign
• trafik işareti = traffic sign

That final -i on işareti is part of the compound. It does not mean accusative here.

Compare:

• otobüs durağı = bus stop
• yatak odası = bedroom
• kahve fincanı = coffee cup

So trafik işareti is the normal way to say traffic sign.

No. Here it is not the accusative.

This is a very common point of confusion.

In trafik işareti, the -i belongs to the noun-compound structure, not to the direct object case. The whole phrase means traffic sign.

Why we know it is not accusative:

• There is no verb here that would take a direct object.
• Trafik işareti is functioning as the subject/topic of the sentence.
• This pattern is standard for compounds made from two nouns.

So think of trafik işareti as one unit of meaning.

Because parkmetrenin is in the genitive case, which often corresponds to of or a possessive relationship.

• parkmetre = parking meter
• parkmetrenin = of the parking meter / the parking meter's

This is used because yanında literally means something like at its side, so Turkish builds the phrase as:

parkmetrenin yanında
= at the parking meter's side
= next to the parking meter

Also, parkmetre ends in a vowel, so the genitive ending appears as -nin:

• araba → arabanın
• masa → masanın
• parkmetre → parkmetrenin

Yanında comes from yan meaning side.

Its structure is roughly:

• yan = side
• yanı = its side
• yanında = at its side

So:

parkmetrenin yanında
literally = at the parking meter's side
natural English = next to the parking meter

This is a very common Turkish pattern with location words such as:

• üstünde = on it / on top of it
• altında = under it
• önünde = in front of it
• arkasında = behind it
• yanında = next to it

Because -da/-de and -a/-e mean different things.

• yanında = at/by next to → location
• yanına = to beside / to the side of → direction or movement toward

So in this sentence, the traffic sign is already located there, which is why Turkish uses yanında.

Compare:

• Trafik işareti parkmetrenin yanında. = The traffic sign is next to the parking meter.
• Arabayı parkmetrenin yanına koydu. = He/She put the car next to the parking meter.

Turkish usually uses postpositions or location nouns rather than English-style prepositions.

English says:

• next to the parking meter

Turkish builds it more like:

• the parking meter's side-at

So instead of putting a word like next to before the noun, Turkish often puts the relationship word after the noun phrase.

That is why learners often see patterns like:

• evin önünde = in front of the house
• masanın üstünde = on the table
• arabanın arkasında = behind the car
• parkmetrenin yanında = next to the parking meter

Turkish does not have a definite article like English the.

So a phrase like trafik işareti can mean:

• the traffic sign
• a traffic sign

The exact meaning depends on context.

In your sentence, English naturally uses the because it sounds like a specific traffic sign and a specific parking meter are being talked about.

If Turkish wants to emphasize a/an, it can use bir:

• Parkmetrenin yanında bir trafik işareti var. = There is a traffic sign next to the parking meter.

So Turkish often leaves article-like meaning to context.

Turkish often puts the most important descriptive information near the end of the sentence. In a sentence like this, the location phrase naturally comes last:

• Trafik işareti = the traffic sign
• parkmetrenin yanında = next to the parking meter

So the structure is basically:

[thing] + [location]

This is very normal for short descriptive sentences in Turkish.

A different order is possible for emphasis, but the given order is straightforward and natural if you are talking about where the traffic sign is.

Yes, and that would also be very natural, but it is slightly different in feel.

• Trafik işareti parkmetrenin yanında.
  = The traffic sign is next to the parking meter.
  This sounds like you are talking about a known traffic sign and stating its location.

• Parkmetrenin yanında trafik işareti var.
  = There is a traffic sign next to the parking meter.
  This sounds more like you are introducing or pointing out the existence of a traffic sign there.

So both are possible, but they are used in slightly different situations.