Parmağım uzun süre aynı yerde kalınca uyuşuyor.

Parmağım means my finger.

It breaks down like this:

• parmak = finger
• -ım = my

So: parmak + ım → parmağım

The k changes to ğ because a vowel-initial suffix is added. This is a very common sound change in Turkish:

• kulak → kulağım = my ear
• ayak → ayağım = my foot
• parmak → parmağım = my finger

Because kalmak usually takes a location in the locative case.

• yer = place
• yerde = in/at the place

So:

• aynı yer = the same place
• aynı yerde = in the same place

With kalmak (to stay/remain), Turkish normally uses -de/-da:

• evde kalmak = to stay at home
• burada kalmak = to stay here
• aynı yerde kalmak = to stay in the same place

In this sentence, aynı yerde can also be understood more naturally in English as in the same position.

Kalınca comes from kalmak (to stay / remain) plus the suffix -ınca / -ince / -unca / -ünce.

Here:

• kalmak = to stay
• kalınca = when it stays / when it remains

This suffix often means:

• when
• once
• sometimes whenever

So aynı yerde kalınca means when it stays in the same place.

In context, it also carries a cause-and-result feeling: when it stays there for a long time, it goes numb.

Both are possible, but they feel a little different.

• kalınca = when it stays / when it has stayed
• kaldığında = when it stays / when it is in the situation of staying

In many everyday sentences, -ınca sounds a bit more natural for a repeated or automatic result:

• Böyle oturunca belim ağrıyor.
  When I sit like this, my back hurts.

It often suggests: X happens, and then Y naturally follows.

So in this sentence, kalınca works very well because the idea is: if my finger stays in one position too long, the result is numbness.

Uyuşuyor comes from uyuşmak.

In this context, uyușmak means:

• to go numb
• to become numb
• to lose feeling

So uyușuyor means it goes numb / it is going numb.

Be careful: depending on context, uyușmak can have other meanings too, such as to match or to agree, but here it clearly means to become numb.

Because Turkish -yor is used more widely than the English present progressive.

In English, is going numb sounds like it is happening right now, but in Turkish -yor can also describe:

• habits
• repeated reactions
• general tendencies
• things that regularly happen

So uyuşuyor here means something like:

• it goes numb
• it gets numb
• it tends to go numb

This is completely normal Turkish.

The subject is parmağım (my finger) for both parts.

Turkish often does not repeat the subject if it is already clear.

So the structure is basically:

• Parmağım ... kalınca = when my finger stays ...
• (parmağım) uyuşuyor = (my finger) goes numb

Turkish avoids repeating words when the meaning is obvious from context.

Because Turkish usually leaves out subject pronouns when they are understood.

English needs it:

• It goes numb

Turkish often does not:

• uyuşuyor

Since parmağım has already been mentioned, Turkish does not need an extra word for it.

This is very normal. Turkish is a pro-drop language, meaning pronouns are often omitted when the meaning is clear.

It is very natural.

Turkish usually puts the main verb at the end, and the -ınca clause comes before it. So the sentence flows like this:

• Parmağım = my finger
• uzun süre = for a long time
• aynı yerde = in the same place
• kalınca = when it stays
• uyuşuyor = goes numb

A more literal English-style gloss would be:

My finger, when it stays in the same place for a long time, goes numb.

Turkish word order is flexible, though, so you could also hear:

• Parmağım aynı yerde uzun süre kalınca uyuşuyor.

That would mean the same thing, with only a slight shift in emphasis.

Uzun süre means for a long time or for an extended period.

• uzun = long
• süre = duration / period

This is a very common expression in Turkish.

Examples:

• Uzun süre bekledim. = I waited for a long time.
• Uzun süre oturunca bacaklarım ağrıyor. = When I sit for a long time, my legs hurt.

In your sentence, uzun süre acts like an adverbial time expression: it tells you how long the finger stays in the same place.

It can mean both, depending on context.

With a body part like parmağım, it very naturally means:

• staying in the same position
• not moving
• remaining fixed in one spot

So even though yer literally means place, the best English translation in this context may be:

• My finger goes numb when it stays in the same position for too long.

That is often more natural than a very literal same place translation.