Learn Turkish: Rakibi mat etmek için vezir fedasından yanayım. - I am in favor of a queen sacrifice to checkmate the opponent.

The postposition yana means "in favor of" or "on the side of," and it always requires the preceding word to take the ablative case (-dan or -den). Here, feda (sacrifice) takes the possessive -sı to form the compound vezir fedası (queen sacrifice). Then, we add the buffer -n- and the ablative -dan, followed by yana with the personal suffix -yım (I am).

Why does rakip (opponent) take the accusative case to become rakibi?

In Turkish, the compound verb mat etmek (to checkmate) takes a direct object. Because the opponent is the specific entity being checkmated, rakip takes the accusative suffix -i. Notice that the final consonant p softens to b (consonant mutation) because it is followed by a vowel.

Doesn't the word vezir usually mean a vizier or government minister?

Yes, historically it means vizier. However, in Turkish chess terminology, the piece known as the "queen" in English is called the vezir.

Why is it vezir fedası instead of just vezir feda?