What caused the conflict between Russia and Austria Hungary?

The immediate cause of the war was the assassination of Archduke Franz Ferdinand of Austria, the heir to the Austro-Hungarian throne, by a Serbian nationalist in Sarajevo (Bosnia) on June 28, 1914.

More profound causes:

1- Growing Russian influence in the Balkans, seen by Austria-Hungary as a threat to its control over Bosnia and Herzegovina, which it had annexed in 1908.

2- Slavic nationalist movements within the Austro-Hungarian Empire that threatened the integrity of the empire.

3- Mutual rivalries among the Great Powers (Germany, Austria-Hungary, Italy, France, Russia, and Great Britain) for influence and power in Europe.

4- Militarism and the arms race among the major European powers, creating a climate of tension and distrust.