The phrase "study at quarrel" has many synonyms to choose from, allowing for a variety of expressions. One option is "examine while disagreeing," which conveys a sense of discord or tension. Another possibility is "analyze amid dispute," which emphasizes a more methodical approach to examining a contentious issue. Alternatively, "investigate in contention" suggests a closer look at a problematic situation. "Research amidst conflict" is another option that signals a more intensive effort to understand a situation in the midst of ongoing disagreement or debate. Ultimately, the choice of synonym depends on the context and the desired connotations, but there are many possibilities for expressing the idea of studying amidst conflict.