Learn Turkish: Bu özellik sadece sana mahsus değil. - This feature is not exclusive to you alone.

The word mahsus (meaning 'exclusive to' or 'reserved for') always requires the preceding noun or pronoun to take the dative case (-(y)e / -(y)a). Because of this rule, 'exclusive to you' becomes sana mahsus.

I've heard mahsus used to mean 'on purpose'. Is that the same word?

Yes, it is the exact same word! In colloquial Turkish, mahsus is often used as an adverb meaning 'intentionally' or 'on purpose' (as in Mahsus mu yapıyorsun? - Are you doing that on purpose?). However, when paired with the dative case as it is here (sana mahsus), it acts as a postposition meaning 'exclusive to' or 'specific to'.

Could I use özgü or has instead of mahsus in this sentence?

Absolutely. Both sana özgü değil and sana has değil mean the exact same thing as sana mahsus değil. Özgü is the native Turkish equivalent, while has and mahsus are of Arabic origin. All three are commonly used and all of them require the dative case.

Since mahsus already means 'exclusive', isn't adding sadece redundant?