Çantadaki mandalinalar senin, buzdolabındaki kayısılar benim.

Çantadaki means the one(s) in the bag or, here, the ... in the bag.

It is built like this:

• çanta = bag
• -da = in / on / at
• -ki = turns the location phrase into something that can describe a noun

So:

• çantada = in the bag
• çantadaki mandalinalar = the tangerines that are in the bag

In other words, -ki helps the phrase act like an adjective.

Because buzdolabı behaves like a compound noun that already contains a possessive-type ending. When Turkish adds another suffix after that kind of form, it often uses a buffer -n-.

So the steps are:

• buzdolabı = refrigerator
• buzdolabında = in the refrigerator
• buzdolabındaki = the one(s) in the refrigerator

That is why you see -ndaki here.

Here, -ki turns a place expression into a modifier.

Compare these:

• çantada mandalinalar var = there are tangerines in the bag
• çantadaki mandalinalar = the tangerines in the bag

Without -ki, you are just saying where something is.
With -ki, you are describing which tangerines you mean.

So -ki is doing something similar to English that are in or just in in phrases like the tangerines in the bag.

In this sentence, senin and benim mean yours and mine.

Literally:

• senin = of you
• benim = of me

But in this kind of sentence, Turkish uses them as the predicate:

• mandalinalar senin = the tangerines are yours
• kayısılar benim = the apricots are mine

So Turkish does not need to repeat a noun like ones. English says yours and mine; Turkish uses senin and benim.

Turkish often leaves out the present-tense to be in third-person sentences like this.

So:

• Çantadaki mandalinalar senin = The tangerines in the bag are yours.
• Buzdolabındaki kayısılar benim = The apricots in the refrigerator are mine.

There is no separate word for are here.

If you want a more emphatic or formal version, Turkish can use:

• senindir
• benimdir

But in everyday Turkish, the shorter version is very normal.

They mean different things:

• mandalinalar senin = the tangerines are yours
• senin mandalinaların = your tangerines

The first is a full statement about ownership.
The second is a noun phrase.

In senin mandalinaların, Turkish uses the regular possessive pattern:

• possessor: senin
• possessed noun with possessive ending: mandalinaların

But in the original sentence, the speaker is not just naming the tangerines. They are saying who they belong to, so mandalinalar senin is the right structure.

Turkish does not have articles like English the or a/an.

Instead, definiteness is usually understood from context or from the structure of the phrase.

So çantadaki mandalinalar naturally means the tangerines in the bag.
The phrase is already specific because çantadaki tells you exactly which tangerines.

-lar is the plural suffix.

So:

• mandalina = tangerine

• mandalinalar = tangerines

• kayısı = apricot
• kayısılar = apricots

It is -lar here because of vowel harmony. After words with back vowels, Turkish uses -lar. After words with front vowels, it uses -ler.

For example:

• ev = house
• evler = houses

Because the number is already shown by the subject noun.

So:

• Kitap senin = The book is yours.
• Kitaplar senin = The books are yours.

The ownership word stays the same.
You do not need a separate plural form of senin or benim here.

Yes, this is a very natural Turkish word order for this kind of sentence.

Pattern:

• subject/topic + predicate

So:

• Çantadaki mandalinalar = the tangerines in the bag
• senin = are yours

Then the second clause mirrors it:

• buzdolabındaki kayısılar = the apricots in the refrigerator
• benim = are mine

The comma joins two parallel clauses and gives a nice contrast: one set is yours, the other is mine.